Data Time Series adalah data yang diperoleh dari pengamatan satu objek dari beberapa periode waktu. Misalnya data jumlah mahasiswa dari tahun ke tahun, data nilai tukar dolar terhadap rupiah, data kasus covid dari bulan januari 2020 sampai periode saat ini, dan masih banyak contoh yang lainnya. Analisis Time Series adalah suatu bentuk peramalan terhadap nilai-nilai dimasa yang akan datang yang didasarkan pada nilai-nilai pada masa lampau. Model ini biasanya digunakan untuk melakukan prediksi/peramalan. Untuk melakukan analisis time series tersebut ada banyak teknik/metode/algoritma/model yang dapat digunakan, berikut beberapa diantaranya:
Secara umum ada 3 komponen time series yaitu:
# Library untuk manipulasi data
library (dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
# Library untuk visualisasi data
library (ggplot2)
library (plotly)
##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
# Library model time series forecasting
library (prophet)
## Loading required package: Rcpp
## Loading required package: rlang
# Library untuk split data
library (caTools)
# Library manipulasi tanggal
library (lubridate)
##
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union
sales <- read.csv("data/train.csv")
head(sales)
# melihat struktur dataset
glimpse (sales)
## Rows: 730,500
## Columns: 4
## $ date <chr> "2013-01-01", "2013-01-02", "2013-01-03", "2013-01-04", "2013-01~
## $ store <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ item <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ sales <int> 13, 11, 14, 13, 10, 12, 10, 9, 12, 9, 9, 7, 10, 12, 5, 7, 16, 7,~
group_sales <- group_by(sales, store)
count(group_sales)
Bisa dilihat bahwa setiap store memiliki 73050 traksaksi.
Sekarang kita akan melihat jumlah transaksi berdasarkan tanggal
transaksi dan kita simpan dalam objek daily_demand
daily_demand <- sales %>%
group_by(date) %>%
summarise(
demand=sum(sales)
)
daily_demand
Kita akan mengambil trankasi pada salah satu store saja, misalnya
pada store 3. dan kita simpan dalam objek
daily_demandstore03 dan rubah data dateke type
tanggal (date)
daily_demandstore03 <- sales %>%
filter (store == "3") %>%
mutate (date = as.Date(date)) %>% #merubah type data date
group_by(date) %>%
summarise(
demand=sum(sales)
)
daily_demandstore03
Bisa dilihat bahwa data date sudah dalam type
tanggal
kita akan memvisualisasi trankasi pada store 03 dari tahun 2013 sampai 2016
plotstore03 <- daily_demandstore03 %>%
ggplot(aes(x = date, y = demand)) +
geom_point(color = "tomato3", group=1) +
labs(
title = "Daily Sales",
subtitle = "Store 03",
caption = "1C Company",
x = "Date",
y = "Total Sales"
) +
theme_minimal()
ggplotly(plotstore03)
Data yang digunakan yaitu data permintaan harian di Store 3 yang
sudah disimpan pada objek daily_demandstore03
daily_demandstore03
Untuk menggunakan algoritma/model Prophet pertama-tama yang harus dilakukan adalah menyiapkan data frame dengan format: ds untuk menyimpan tanggal, dan y untuk menyimpan dari nilai yang akan prediksi.
# Menyiapkan data
train_daily_3 <- daily_demandstore03 %>%
rename(
ds = "date",
y = "demand"
)
glimpse(train_daily_3)
## Rows: 1,461
## Columns: 2
## $ ds <date> 2013-01-01, 2013-01-02, 2013-01-03, 2013-01-04, 2013-01-05, 2013-0~
## $ y <int> 1588, 1538, 1635, 1741, 1887, 1956, 1313, 1538, 1633, 1677, 1831, 1~
Melakukan pemodelan data training dengan menggunakan fungsi
fit.prophet() dimana sebelumnya kita harus menentukan
seasonality nya. dalam kasus ini kita mengggunakan
daily.seasonality
# fitting model data training
model_ts <- prophet(daily.seasonality = TRUE, seasonality_prior_scale=0.1) %>%
fit.prophet(train_daily_3)
model_ts
## $growth
## [1] "linear"
##
## $changepoints
## [1] "2013-02-17 GMT" "2013-04-04 GMT" "2013-05-21 GMT" "2013-07-07 GMT"
## [5] "2013-08-22 GMT" "2013-10-08 GMT" "2013-11-24 GMT" "2014-01-09 GMT"
## [9] "2014-02-25 GMT" "2014-04-13 GMT" "2014-05-29 GMT" "2014-07-15 GMT"
## [13] "2014-08-31 GMT" "2014-10-17 GMT" "2014-12-02 GMT" "2015-01-18 GMT"
## [17] "2015-03-06 GMT" "2015-04-21 GMT" "2015-06-07 GMT" "2015-07-24 GMT"
## [21] "2015-09-08 GMT" "2015-10-25 GMT" "2015-12-11 GMT" "2016-01-26 GMT"
## [25] "2016-03-13 GMT"
##
## $n.changepoints
## [1] 25
##
## $changepoint.range
## [1] 0.8
##
## $yearly.seasonality
## [1] "auto"
##
## $weekly.seasonality
## [1] "auto"
##
## $daily.seasonality
## [1] TRUE
##
## $holidays
## NULL
##
## $seasonality.mode
## [1] "additive"
##
## $seasonality.prior.scale
## [1] 10
##
## $changepoint.prior.scale
## [1] 0.05
##
## $holidays.prior.scale
## [1] 10
##
## $mcmc.samples
## [1] 0
##
## $interval.width
## [1] 0.8
##
## $uncertainty.samples
## [1] 1000
##
## $specified.changepoints
## [1] FALSE
##
## $start
## [1] "2013-01-01 GMT"
##
## $y.scale
## [1] 5004
##
## $logistic.floor
## [1] FALSE
##
## $t.scale
## [1] 126144000
##
## $changepoints.t
## [1] 0.03219178 0.06369863 0.09589041 0.12808219 0.15958904 0.19178082
## [7] 0.22397260 0.25547945 0.28767123 0.31986301 0.35136986 0.38356164
## [13] 0.41575342 0.44794521 0.47945205 0.51164384 0.54383562 0.57534247
## [19] 0.60753425 0.63972603 0.67123288 0.70342466 0.73561644 0.76712329
## [25] 0.79931507
##
## $seasonalities
## $seasonalities$yearly
## $seasonalities$yearly$period
## [1] 365.25
##
## $seasonalities$yearly$fourier.order
## [1] 10
##
## $seasonalities$yearly$prior.scale
## [1] 10
##
## $seasonalities$yearly$mode
## [1] "additive"
##
## $seasonalities$yearly$condition.name
## NULL
##
##
## $seasonalities$weekly
## $seasonalities$weekly$period
## [1] 7
##
## $seasonalities$weekly$fourier.order
## [1] 3
##
## $seasonalities$weekly$prior.scale
## [1] 10
##
## $seasonalities$weekly$mode
## [1] "additive"
##
## $seasonalities$weekly$condition.name
## NULL
##
##
## $seasonalities$daily
## $seasonalities$daily$period
## [1] 1
##
## $seasonalities$daily$fourier.order
## [1] 4
##
## $seasonalities$daily$prior.scale
## [1] 10
##
## $seasonalities$daily$mode
## [1] "additive"
##
## $seasonalities$daily$condition.name
## NULL
##
##
##
## $extra_regressors
## list()
##
## $country_holidays
## NULL
##
## $stan.fit
## $stan.fit$par
## $stan.fit$par$k
## [1] -0.3295687
##
## $stan.fit$par$m
## [1] 0.3550251
##
## $stan.fit$par$delta
## [1] 1.256203e-07 -2.981828e-08 2.662971e-01 4.727642e-01 1.918457e-01
## [6] -1.123155e-07 5.084654e-08 -2.085096e-01 -2.661333e-01 2.654932e-08
## [11] -3.862036e-09 1.096295e-07 -4.993257e-09 -1.140498e-02 -2.853337e-02
## [16] -2.476382e-08 1.702067e-07 7.699039e-03 3.470921e-03 4.823478e-02
## [21] 7.679313e-02 2.522520e-02 3.485977e-08 3.816875e-08 -6.489775e-02
##
## $stan.fit$par$sigma_obs
## [1] 0.02706113
##
## $stan.fit$par$beta
## [1] -1.495432e-02 -1.393878e-01 -2.409588e-02 -7.911498e-03 -1.775391e-02
## [6] -2.432144e-02 7.720784e-03 -8.146249e-03 6.691417e-03 -1.189065e-02
## [11] 1.537089e-02 3.035046e-03 3.266428e-03 9.648419e-03 4.178968e-03
## [16] 5.075157e-03 -7.409245e-03 5.949041e-03 -4.866335e-03 -4.556570e-04
## [21] 7.696754e-02 -2.570954e-03 -4.462192e-02 -9.995636e-03 4.729545e-02
## [26] 6.687884e-03 -5.301163e-11 3.808422e-02 -1.060233e-10 3.808422e-02
## [31] -2.660458e-11 3.808422e-02 -2.120465e-10 3.808422e-02
##
## $stan.fit$par$trend
## [1] 0.3550251 0.3547994 0.3545736 0.3543479 0.3541222 0.3538964 0.3536707
## [8] 0.3534450 0.3532192 0.3529935 0.3527678 0.3525420 0.3523163 0.3520906
## [15] 0.3518649 0.3516391 0.3514134 0.3511877 0.3509619 0.3507362 0.3505105
## [22] 0.3502847 0.3500590 0.3498333 0.3496075 0.3493818 0.3491561 0.3489303
## [29] 0.3487046 0.3484789 0.3482531 0.3480274 0.3478017 0.3475759 0.3473502
## [36] 0.3471245 0.3468987 0.3466730 0.3464473 0.3462216 0.3459958 0.3457701
## [43] 0.3455444 0.3453186 0.3450929 0.3448672 0.3446414 0.3444157 0.3441900
## [50] 0.3439642 0.3437385 0.3435128 0.3432870 0.3430613 0.3428356 0.3426098
## [57] 0.3423841 0.3421584 0.3419326 0.3417069 0.3414812 0.3412555 0.3410297
## [64] 0.3408040 0.3405783 0.3403525 0.3401268 0.3399011 0.3396753 0.3394496
## [71] 0.3392239 0.3389981 0.3387724 0.3385467 0.3383209 0.3380952 0.3378695
## [78] 0.3376437 0.3374180 0.3371923 0.3369665 0.3367408 0.3365151 0.3362893
## [85] 0.3360636 0.3358379 0.3356122 0.3353864 0.3351607 0.3349350 0.3347092
## [92] 0.3344835 0.3342578 0.3340320 0.3338063 0.3335806 0.3333548 0.3331291
## [99] 0.3329034 0.3326776 0.3324519 0.3322262 0.3320004 0.3317747 0.3315490
## [106] 0.3313232 0.3310975 0.3308718 0.3306461 0.3304203 0.3301946 0.3299689
## [113] 0.3297431 0.3295174 0.3292917 0.3290659 0.3288402 0.3286145 0.3283887
## [120] 0.3281630 0.3279373 0.3277115 0.3274858 0.3272601 0.3270343 0.3268086
## [127] 0.3265829 0.3263571 0.3261314 0.3259057 0.3256799 0.3254542 0.3252285
## [134] 0.3250028 0.3247770 0.3245513 0.3243256 0.3240998 0.3238741 0.3236484
## [141] 0.3234226 0.3233793 0.3233360 0.3232926 0.3232493 0.3232059 0.3231626
## [148] 0.3231193 0.3230759 0.3230326 0.3229893 0.3229459 0.3229026 0.3228593
## [155] 0.3228159 0.3227726 0.3227292 0.3226859 0.3226426 0.3225992 0.3225559
## [162] 0.3225126 0.3224692 0.3224259 0.3223826 0.3223392 0.3222959 0.3222525
## [169] 0.3222092 0.3221659 0.3221225 0.3220792 0.3220359 0.3219925 0.3219492
## [176] 0.3219058 0.3218625 0.3218192 0.3217758 0.3217325 0.3216892 0.3216458
## [183] 0.3216025 0.3215592 0.3215158 0.3214725 0.3214291 0.3213858 0.3216663
## [190] 0.3219468 0.3222272 0.3225077 0.3227882 0.3230687 0.3233491 0.3236296
## [197] 0.3239101 0.3241906 0.3244710 0.3247515 0.3250320 0.3253125 0.3255929
## [204] 0.3258734 0.3261539 0.3264343 0.3267148 0.3269953 0.3272758 0.3275562
## [211] 0.3278367 0.3281172 0.3283977 0.3286781 0.3289586 0.3292391 0.3295196
## [218] 0.3298000 0.3300805 0.3303610 0.3306415 0.3309219 0.3312024 0.3314829
## [225] 0.3317634 0.3320438 0.3323243 0.3326048 0.3328853 0.3331657 0.3334462
## [232] 0.3337267 0.3340072 0.3342876 0.3346995 0.3351114 0.3355233 0.3359351
## [239] 0.3363470 0.3367589 0.3371708 0.3375826 0.3379945 0.3384064 0.3388183
## [246] 0.3392301 0.3396420 0.3400539 0.3404658 0.3408776 0.3412895 0.3417014
## [253] 0.3421133 0.3425251 0.3429370 0.3433489 0.3437608 0.3441726 0.3445845
## [260] 0.3449964 0.3454083 0.3458201 0.3462320 0.3466439 0.3470558 0.3474677
## [267] 0.3478795 0.3482914 0.3487033 0.3491152 0.3495270 0.3499389 0.3503508
## [274] 0.3507627 0.3511745 0.3515864 0.3519983 0.3524102 0.3528220 0.3532339
## [281] 0.3536458 0.3540577 0.3544695 0.3548814 0.3552933 0.3557052 0.3561170
## [288] 0.3565289 0.3569408 0.3573527 0.3577645 0.3581764 0.3585883 0.3590002
## [295] 0.3594120 0.3598239 0.3602358 0.3606477 0.3610595 0.3614714 0.3618833
## [302] 0.3622952 0.3627070 0.3631189 0.3635308 0.3639427 0.3643546 0.3647664
## [309] 0.3651783 0.3655902 0.3660021 0.3664139 0.3668258 0.3672377 0.3676496
## [316] 0.3680614 0.3684733 0.3688852 0.3692971 0.3697089 0.3701208 0.3705327
## [323] 0.3709446 0.3713564 0.3717683 0.3721802 0.3725921 0.3730039 0.3734158
## [330] 0.3738277 0.3742396 0.3746514 0.3750633 0.3754752 0.3758871 0.3762989
## [337] 0.3767108 0.3771227 0.3775346 0.3779464 0.3783583 0.3787702 0.3791821
## [344] 0.3795939 0.3800058 0.3804177 0.3808296 0.3812414 0.3816533 0.3820652
## [351] 0.3824771 0.3828890 0.3833008 0.3837127 0.3841246 0.3845365 0.3849483
## [358] 0.3853602 0.3857721 0.3861840 0.3865958 0.3870077 0.3874196 0.3878315
## [365] 0.3882433 0.3886552 0.3890671 0.3894790 0.3898908 0.3903027 0.3907146
## [372] 0.3911265 0.3915383 0.3919502 0.3922193 0.3924883 0.3927574 0.3930265
## [379] 0.3932955 0.3935646 0.3938336 0.3941027 0.3943718 0.3946408 0.3949099
## [386] 0.3951789 0.3954480 0.3957171 0.3959861 0.3962552 0.3965242 0.3967933
## [393] 0.3970624 0.3973314 0.3976005 0.3978696 0.3981386 0.3984077 0.3986767
## [400] 0.3989458 0.3992149 0.3994839 0.3997530 0.4000220 0.4002911 0.4005602
## [407] 0.4008292 0.4010983 0.4013673 0.4016364 0.4019055 0.4021745 0.4024436
## [414] 0.4027126 0.4029817 0.4032508 0.4035198 0.4037889 0.4040580 0.4043270
## [421] 0.4045961 0.4046829 0.4047696 0.4048564 0.4049432 0.4050300 0.4051167
## [428] 0.4052035 0.4052903 0.4053771 0.4054638 0.4055506 0.4056374 0.4057242
## [435] 0.4058110 0.4058977 0.4059845 0.4060713 0.4061581 0.4062448 0.4063316
## [442] 0.4064184 0.4065052 0.4065920 0.4066787 0.4067655 0.4068523 0.4069391
## [449] 0.4070258 0.4071126 0.4071994 0.4072862 0.4073730 0.4074597 0.4075465
## [456] 0.4076333 0.4077201 0.4078068 0.4078936 0.4079804 0.4080672 0.4081540
## [463] 0.4082407 0.4083275 0.4084143 0.4085011 0.4085878 0.4086746 0.4087614
## [470] 0.4088482 0.4089350 0.4090217 0.4091085 0.4091953 0.4092821 0.4093688
## [477] 0.4094556 0.4095424 0.4096292 0.4097160 0.4098027 0.4098895 0.4099763
## [484] 0.4100631 0.4101498 0.4102366 0.4103234 0.4104102 0.4104970 0.4105837
## [491] 0.4106705 0.4107573 0.4108441 0.4109308 0.4110176 0.4111044 0.4111912
## [498] 0.4112780 0.4113647 0.4114515 0.4115383 0.4116251 0.4117118 0.4117986
## [505] 0.4118854 0.4119722 0.4120590 0.4121457 0.4122325 0.4123193 0.4124061
## [512] 0.4124928 0.4125796 0.4126664 0.4127532 0.4128400 0.4129267 0.4130135
## [519] 0.4131003 0.4131871 0.4132738 0.4133606 0.4134474 0.4135342 0.4136210
## [526] 0.4137077 0.4137945 0.4138813 0.4139681 0.4140548 0.4141416 0.4142284
## [533] 0.4143152 0.4144020 0.4144887 0.4145755 0.4146623 0.4147491 0.4148358
## [540] 0.4149226 0.4150094 0.4150962 0.4151830 0.4152697 0.4153565 0.4154433
## [547] 0.4155301 0.4156168 0.4157036 0.4157904 0.4158772 0.4159640 0.4160507
## [554] 0.4161375 0.4162243 0.4163111 0.4163978 0.4164846 0.4165714 0.4166582
## [561] 0.4167450 0.4168317 0.4169185 0.4170053 0.4170921 0.4171788 0.4172656
## [568] 0.4173524 0.4174392 0.4175260 0.4176127 0.4176995 0.4177863 0.4178731
## [575] 0.4179598 0.4180466 0.4181334 0.4182202 0.4183070 0.4183937 0.4184805
## [582] 0.4185673 0.4186541 0.4187408 0.4188276 0.4189144 0.4190012 0.4190880
## [589] 0.4191747 0.4192615 0.4193483 0.4194351 0.4195218 0.4196086 0.4196954
## [596] 0.4197822 0.4198690 0.4199557 0.4200425 0.4201293 0.4202161 0.4203028
## [603] 0.4203896 0.4204764 0.4205632 0.4206500 0.4207367 0.4208235 0.4209103
## [610] 0.4209971 0.4210838 0.4211706 0.4212574 0.4213442 0.4214310 0.4215177
## [617] 0.4216045 0.4216913 0.4217781 0.4218648 0.4219516 0.4220384 0.4221252
## [624] 0.4222120 0.4222987 0.4223855 0.4224723 0.4225591 0.4226458 0.4227326
## [631] 0.4228194 0.4229062 0.4229930 0.4230797 0.4231665 0.4232533 0.4233401
## [638] 0.4234268 0.4235136 0.4236004 0.4236872 0.4237740 0.4238607 0.4239475
## [645] 0.4240343 0.4241211 0.4242078 0.4242946 0.4243814 0.4244682 0.4245550
## [652] 0.4246417 0.4247285 0.4248153 0.4249021 0.4249810 0.4250600 0.4251390
## [659] 0.4252179 0.4252969 0.4253759 0.4254548 0.4255338 0.4256128 0.4256917
## [666] 0.4257707 0.4258497 0.4259286 0.4260076 0.4260866 0.4261655 0.4262445
## [673] 0.4263235 0.4264024 0.4264814 0.4265604 0.4266393 0.4267183 0.4267973
## [680] 0.4268762 0.4269552 0.4270342 0.4271131 0.4271921 0.4272711 0.4273500
## [687] 0.4274290 0.4275080 0.4275869 0.4276659 0.4277449 0.4278238 0.4279028
## [694] 0.4279818 0.4280607 0.4281397 0.4282187 0.4282976 0.4283766 0.4284555
## [701] 0.4285345 0.4285939 0.4286534 0.4287128 0.4287722 0.4288316 0.4288911
## [708] 0.4289505 0.4290099 0.4290693 0.4291287 0.4291882 0.4292476 0.4293070
## [715] 0.4293664 0.4294259 0.4294853 0.4295447 0.4296041 0.4296635 0.4297230
## [722] 0.4297824 0.4298418 0.4299012 0.4299607 0.4300201 0.4300795 0.4301389
## [729] 0.4301984 0.4302578 0.4303172 0.4303766 0.4304360 0.4304955 0.4305549
## [736] 0.4306143 0.4306737 0.4307332 0.4307926 0.4308520 0.4309114 0.4309708
## [743] 0.4310303 0.4310897 0.4311491 0.4312085 0.4312680 0.4313274 0.4313868
## [750] 0.4314462 0.4315057 0.4315651 0.4316245 0.4316839 0.4317433 0.4318028
## [757] 0.4318622 0.4319216 0.4319810 0.4320405 0.4320999 0.4321593 0.4322187
## [764] 0.4322781 0.4323376 0.4323970 0.4324564 0.4325158 0.4325753 0.4326347
## [771] 0.4326941 0.4327535 0.4328130 0.4328724 0.4329318 0.4329912 0.4330506
## [778] 0.4331101 0.4331695 0.4332289 0.4332883 0.4333478 0.4334072 0.4334666
## [785] 0.4335260 0.4335855 0.4336449 0.4337043 0.4337637 0.4338231 0.4338826
## [792] 0.4339420 0.4340014 0.4340608 0.4341203 0.4341797 0.4342391 0.4342985
## [799] 0.4343579 0.4344174 0.4344768 0.4345362 0.4345956 0.4346551 0.4347145
## [806] 0.4347739 0.4348333 0.4348928 0.4349522 0.4350116 0.4350710 0.4351304
## [813] 0.4351899 0.4352493 0.4353087 0.4353681 0.4354276 0.4354870 0.4355464
## [820] 0.4356058 0.4356653 0.4357247 0.4357841 0.4358435 0.4359029 0.4359624
## [827] 0.4360218 0.4360812 0.4361406 0.4362001 0.4362595 0.4363189 0.4363783
## [834] 0.4364377 0.4364972 0.4365566 0.4366160 0.4366754 0.4367349 0.4367943
## [841] 0.4368537 0.4369184 0.4369831 0.4370478 0.4371125 0.4371772 0.4372419
## [848] 0.4373066 0.4373713 0.4374360 0.4375007 0.4375654 0.4376301 0.4376948
## [855] 0.4377595 0.4378242 0.4378888 0.4379535 0.4380182 0.4380829 0.4381476
## [862] 0.4382123 0.4382770 0.4383417 0.4384064 0.4384711 0.4385358 0.4386005
## [869] 0.4386652 0.4387299 0.4387946 0.4388593 0.4389240 0.4389887 0.4390534
## [876] 0.4391181 0.4391828 0.4392475 0.4393122 0.4393769 0.4394416 0.4395063
## [883] 0.4395709 0.4396356 0.4397003 0.4397650 0.4398297 0.4398944 0.4399615
## [890] 0.4400286 0.4400956 0.4401627 0.4402298 0.4402969 0.4403639 0.4404310
## [897] 0.4404981 0.4405652 0.4406322 0.4406993 0.4407664 0.4408335 0.4409005
## [904] 0.4409676 0.4410347 0.4411018 0.4411688 0.4412359 0.4413030 0.4413700
## [911] 0.4414371 0.4415042 0.4415713 0.4416383 0.4417054 0.4417725 0.4418396
## [918] 0.4419066 0.4419737 0.4420408 0.4421079 0.4421749 0.4422420 0.4423091
## [925] 0.4423761 0.4424432 0.4425103 0.4425774 0.4426444 0.4427115 0.4427786
## [932] 0.4428457 0.4429127 0.4429798 0.4430469 0.4431470 0.4432471 0.4433472
## [939] 0.4434473 0.4435474 0.4436476 0.4437477 0.4438478 0.4439479 0.4440480
## [946] 0.4441481 0.4442482 0.4443483 0.4444484 0.4445486 0.4446487 0.4447488
## [953] 0.4448489 0.4449490 0.4450491 0.4451492 0.4452493 0.4453494 0.4454496
## [960] 0.4455497 0.4456498 0.4457499 0.4458500 0.4459501 0.4460502 0.4461503
## [967] 0.4462504 0.4463505 0.4464507 0.4465508 0.4466509 0.4467510 0.4468511
## [974] 0.4469512 0.4470513 0.4471514 0.4472515 0.4473517 0.4474518 0.4475519
## [981] 0.4476520 0.4478047 0.4479574 0.4481101 0.4482628 0.4484155 0.4485682
## [988] 0.4487210 0.4488737 0.4490264 0.4491791 0.4493318 0.4494845 0.4496372
## [995] 0.4497899 0.4499426 0.4500953 0.4502480 0.4504008 0.4505535 0.4507062
## [1002] 0.4508589 0.4510116 0.4511643 0.4513170 0.4514697 0.4516224 0.4517751
## [1009] 0.4519278 0.4520806 0.4522333 0.4523860 0.4525387 0.4526914 0.4528441
## [1016] 0.4529968 0.4531495 0.4533022 0.4534549 0.4536076 0.4537604 0.4539131
## [1023] 0.4540658 0.4542185 0.4543712 0.4545239 0.4546766 0.4548293 0.4549993
## [1030] 0.4551693 0.4553393 0.4555093 0.4556793 0.4558492 0.4560192 0.4561892
## [1037] 0.4563592 0.4565292 0.4566992 0.4568692 0.4570391 0.4572091 0.4573791
## [1044] 0.4575491 0.4577191 0.4578891 0.4580591 0.4582291 0.4583990 0.4585690
## [1051] 0.4587390 0.4589090 0.4590790 0.4592490 0.4594190 0.4595889 0.4597589
## [1058] 0.4599289 0.4600989 0.4602689 0.4604389 0.4606089 0.4607789 0.4609488
## [1065] 0.4611188 0.4612888 0.4614588 0.4616288 0.4617988 0.4619688 0.4621387
## [1072] 0.4623087 0.4624787 0.4626487 0.4628187 0.4629887 0.4631587 0.4633287
## [1079] 0.4634986 0.4636686 0.4638386 0.4640086 0.4641786 0.4643486 0.4645186
## [1086] 0.4646885 0.4648585 0.4650285 0.4651985 0.4653685 0.4655385 0.4657085
## [1093] 0.4658785 0.4660484 0.4662184 0.4663884 0.4665584 0.4667284 0.4668984
## [1100] 0.4670684 0.4672383 0.4674083 0.4675783 0.4677483 0.4679183 0.4680883
## [1107] 0.4682583 0.4684283 0.4685982 0.4687682 0.4689382 0.4691082 0.4692782
## [1114] 0.4694482 0.4696182 0.4697881 0.4699581 0.4701281 0.4702981 0.4704681
## [1121] 0.4706381 0.4708081 0.4709781 0.4711480 0.4713180 0.4714880 0.4716580
## [1128] 0.4718280 0.4719980 0.4721680 0.4723379 0.4725079 0.4726779 0.4728479
## [1135] 0.4730179 0.4731879 0.4733579 0.4735279 0.4736978 0.4738678 0.4740378
## [1142] 0.4742078 0.4743778 0.4745478 0.4747178 0.4748877 0.4750577 0.4752277
## [1149] 0.4753977 0.4755677 0.4757377 0.4759077 0.4760777 0.4762476 0.4764176
## [1156] 0.4765876 0.4767576 0.4769276 0.4770976 0.4772676 0.4774375 0.4776075
## [1163] 0.4777775 0.4779475 0.4781175 0.4782875 0.4784575 0.4786275 0.4787530
## [1170] 0.4788785 0.4790041 0.4791296 0.4792551 0.4793807 0.4795062 0.4796317
## [1177] 0.4797573 0.4798828 0.4800084 0.4801339 0.4802594 0.4803850 0.4805105
## [1184] 0.4806360 0.4807616 0.4808871 0.4810126 0.4811382 0.4812637 0.4813892
## [1191] 0.4815148 0.4816403 0.4817659 0.4818914 0.4820169 0.4821425 0.4822680
## [1198] 0.4823935 0.4825191 0.4826446 0.4827701 0.4828957 0.4830212 0.4831468
## [1205] 0.4832723 0.4833978 0.4835234 0.4836489 0.4837744 0.4839000 0.4840255
## [1212] 0.4841510 0.4842766 0.4844021 0.4845277 0.4846532 0.4847787 0.4849043
## [1219] 0.4850298 0.4851553 0.4852809 0.4854064 0.4855319 0.4856575 0.4857830
## [1226] 0.4859086 0.4860341 0.4861596 0.4862852 0.4864107 0.4865362 0.4866618
## [1233] 0.4867873 0.4869128 0.4870384 0.4871639 0.4872894 0.4874150 0.4875405
## [1240] 0.4876661 0.4877916 0.4879171 0.4880427 0.4881682 0.4882937 0.4884193
## [1247] 0.4885448 0.4886703 0.4887959 0.4889214 0.4890470 0.4891725 0.4892980
## [1254] 0.4894236 0.4895491 0.4896746 0.4898002 0.4899257 0.4900512 0.4901768
## [1261] 0.4903023 0.4904279 0.4905534 0.4906789 0.4908045 0.4909300 0.4910555
## [1268] 0.4911811 0.4913066 0.4914321 0.4915577 0.4916832 0.4918088 0.4919343
## [1275] 0.4920598 0.4921854 0.4923109 0.4924364 0.4925620 0.4926875 0.4928130
## [1282] 0.4929386 0.4930641 0.4931896 0.4933152 0.4934407 0.4935663 0.4936918
## [1289] 0.4938173 0.4939429 0.4940684 0.4941939 0.4943195 0.4944450 0.4945705
## [1296] 0.4946961 0.4948216 0.4949472 0.4950727 0.4951982 0.4953238 0.4954493
## [1303] 0.4955748 0.4957004 0.4958259 0.4959514 0.4960770 0.4962025 0.4963281
## [1310] 0.4964536 0.4965791 0.4967047 0.4968302 0.4969557 0.4970813 0.4972068
## [1317] 0.4973323 0.4974579 0.4975834 0.4977090 0.4978345 0.4979600 0.4980856
## [1324] 0.4982111 0.4983366 0.4984622 0.4985877 0.4987132 0.4988388 0.4989643
## [1331] 0.4990898 0.4992154 0.4993409 0.4994665 0.4995920 0.4997175 0.4998431
## [1338] 0.4999686 0.5000941 0.5002197 0.5003452 0.5004707 0.5005963 0.5007218
## [1345] 0.5008474 0.5009729 0.5010984 0.5012240 0.5013495 0.5014750 0.5016006
## [1352] 0.5017261 0.5018516 0.5019772 0.5021027 0.5022283 0.5023538 0.5024793
## [1359] 0.5026049 0.5027304 0.5028559 0.5029815 0.5031070 0.5032325 0.5033581
## [1366] 0.5034836 0.5036092 0.5037347 0.5038602 0.5039858 0.5041113 0.5042368
## [1373] 0.5043624 0.5044879 0.5046134 0.5047390 0.5048645 0.5049900 0.5051156
## [1380] 0.5052411 0.5053667 0.5054922 0.5056177 0.5057433 0.5058688 0.5059943
## [1387] 0.5061199 0.5062454 0.5063709 0.5064965 0.5066220 0.5067476 0.5068731
## [1394] 0.5069986 0.5071242 0.5072497 0.5073752 0.5075008 0.5076263 0.5077518
## [1401] 0.5078774 0.5080029 0.5081285 0.5082540 0.5083795 0.5085051 0.5086306
## [1408] 0.5087561 0.5088817 0.5090072 0.5091327 0.5092583 0.5093838 0.5095094
## [1415] 0.5096349 0.5097604 0.5098860 0.5100115 0.5101370 0.5102626 0.5103881
## [1422] 0.5105136 0.5106392 0.5107647 0.5108902 0.5110158 0.5111413 0.5112669
## [1429] 0.5113924 0.5115179 0.5116435 0.5117690 0.5118945 0.5120201 0.5121456
## [1436] 0.5122711 0.5123967 0.5125222 0.5126478 0.5127733 0.5128988 0.5130244
## [1443] 0.5131499 0.5132754 0.5134010 0.5135265 0.5136520 0.5137776 0.5139031
## [1450] 0.5140287 0.5141542 0.5142797 0.5144053 0.5145308 0.5146563 0.5147819
## [1457] 0.5149074 0.5150329 0.5151585 0.5152840 0.5154095
##
##
## $stan.fit$value
## [1] 4510.003
##
## $stan.fit$return_code
## [1] 0
##
## $stan.fit$theta_tilde
## k m delta[1] delta[2] delta[3] delta[4]
## [1,] -0.3295687 0.3550251 1.256203e-07 -2.981828e-08 0.2662971 0.4727642
## delta[5] delta[6] delta[7] delta[8] delta[9] delta[10]
## [1,] 0.1918457 -1.123155e-07 5.084654e-08 -0.2085096 -0.2661333 2.654932e-08
## delta[11] delta[12] delta[13] delta[14] delta[15]
## [1,] -3.862036e-09 1.096295e-07 -4.993257e-09 -0.01140498 -0.02853337
## delta[16] delta[17] delta[18] delta[19] delta[20] delta[21]
## [1,] -2.476382e-08 1.702067e-07 0.007699039 0.003470921 0.04823478 0.07679313
## delta[22] delta[23] delta[24] delta[25] sigma_obs beta[1]
## [1,] 0.0252252 3.485977e-08 3.816875e-08 -0.06489775 0.02706113 -0.01495432
## beta[2] beta[3] beta[4] beta[5] beta[6] beta[7]
## [1,] -0.1393878 -0.02409588 -0.007911498 -0.01775391 -0.02432144 0.007720784
## beta[8] beta[9] beta[10] beta[11] beta[12] beta[13]
## [1,] -0.008146249 0.006691417 -0.01189065 0.01537089 0.003035046 0.003266428
## beta[14] beta[15] beta[16] beta[17] beta[18] beta[19]
## [1,] 0.009648419 0.004178968 0.005075157 -0.007409245 0.005949041 -0.004866335
## beta[20] beta[21] beta[22] beta[23] beta[24] beta[25]
## [1,] -0.000455657 0.07696754 -0.002570954 -0.04462192 -0.009995636 0.04729545
## beta[26] beta[27] beta[28] beta[29] beta[30]
## [1,] 0.006687884 -5.301163e-11 0.03808422 -1.060233e-10 0.03808422
## beta[31] beta[32] beta[33] beta[34] trend[1] trend[2]
## [1,] -2.660458e-11 0.03808422 -2.120465e-10 0.03808422 0.3550251 0.3547994
## trend[3] trend[4] trend[5] trend[6] trend[7] trend[8] trend[9]
## [1,] 0.3545736 0.3543479 0.3541222 0.3538964 0.3536707 0.353445 0.3532192
## trend[10] trend[11] trend[12] trend[13] trend[14] trend[15] trend[16]
## [1,] 0.3529935 0.3527678 0.352542 0.3523163 0.3520906 0.3518649 0.3516391
## trend[17] trend[18] trend[19] trend[20] trend[21] trend[22] trend[23]
## [1,] 0.3514134 0.3511877 0.3509619 0.3507362 0.3505105 0.3502847 0.350059
## trend[24] trend[25] trend[26] trend[27] trend[28] trend[29] trend[30]
## [1,] 0.3498333 0.3496075 0.3493818 0.3491561 0.3489303 0.3487046 0.3484789
## trend[31] trend[32] trend[33] trend[34] trend[35] trend[36] trend[37]
## [1,] 0.3482531 0.3480274 0.3478017 0.3475759 0.3473502 0.3471245 0.3468987
## trend[38] trend[39] trend[40] trend[41] trend[42] trend[43] trend[44]
## [1,] 0.346673 0.3464473 0.3462216 0.3459958 0.3457701 0.3455444 0.3453186
## trend[45] trend[46] trend[47] trend[48] trend[49] trend[50] trend[51]
## [1,] 0.3450929 0.3448672 0.3446414 0.3444157 0.34419 0.3439642 0.3437385
## trend[52] trend[53] trend[54] trend[55] trend[56] trend[57] trend[58]
## [1,] 0.3435128 0.343287 0.3430613 0.3428356 0.3426098 0.3423841 0.3421584
## trend[59] trend[60] trend[61] trend[62] trend[63] trend[64] trend[65]
## [1,] 0.3419326 0.3417069 0.3414812 0.3412555 0.3410297 0.340804 0.3405783
## trend[66] trend[67] trend[68] trend[69] trend[70] trend[71] trend[72]
## [1,] 0.3403525 0.3401268 0.3399011 0.3396753 0.3394496 0.3392239 0.3389981
## trend[73] trend[74] trend[75] trend[76] trend[77] trend[78] trend[79]
## [1,] 0.3387724 0.3385467 0.3383209 0.3380952 0.3378695 0.3376437 0.337418
## trend[80] trend[81] trend[82] trend[83] trend[84] trend[85] trend[86]
## [1,] 0.3371923 0.3369665 0.3367408 0.3365151 0.3362893 0.3360636 0.3358379
## trend[87] trend[88] trend[89] trend[90] trend[91] trend[92] trend[93]
## [1,] 0.3356122 0.3353864 0.3351607 0.334935 0.3347092 0.3344835 0.3342578
## trend[94] trend[95] trend[96] trend[97] trend[98] trend[99] trend[100]
## [1,] 0.334032 0.3338063 0.3335806 0.3333548 0.3331291 0.3329034 0.3326776
## trend[101] trend[102] trend[103] trend[104] trend[105] trend[106]
## [1,] 0.3324519 0.3322262 0.3320004 0.3317747 0.331549 0.3313232
## trend[107] trend[108] trend[109] trend[110] trend[111] trend[112]
## [1,] 0.3310975 0.3308718 0.3306461 0.3304203 0.3301946 0.3299689
## trend[113] trend[114] trend[115] trend[116] trend[117] trend[118]
## [1,] 0.3297431 0.3295174 0.3292917 0.3290659 0.3288402 0.3286145
## trend[119] trend[120] trend[121] trend[122] trend[123] trend[124]
## [1,] 0.3283887 0.328163 0.3279373 0.3277115 0.3274858 0.3272601
## trend[125] trend[126] trend[127] trend[128] trend[129] trend[130]
## [1,] 0.3270343 0.3268086 0.3265829 0.3263571 0.3261314 0.3259057
## trend[131] trend[132] trend[133] trend[134] trend[135] trend[136]
## [1,] 0.3256799 0.3254542 0.3252285 0.3250028 0.324777 0.3245513
## trend[137] trend[138] trend[139] trend[140] trend[141] trend[142]
## [1,] 0.3243256 0.3240998 0.3238741 0.3236484 0.3234226 0.3233793
## trend[143] trend[144] trend[145] trend[146] trend[147] trend[148]
## [1,] 0.323336 0.3232926 0.3232493 0.3232059 0.3231626 0.3231193
## trend[149] trend[150] trend[151] trend[152] trend[153] trend[154]
## [1,] 0.3230759 0.3230326 0.3229893 0.3229459 0.3229026 0.3228593
## trend[155] trend[156] trend[157] trend[158] trend[159] trend[160]
## [1,] 0.3228159 0.3227726 0.3227292 0.3226859 0.3226426 0.3225992
## trend[161] trend[162] trend[163] trend[164] trend[165] trend[166]
## [1,] 0.3225559 0.3225126 0.3224692 0.3224259 0.3223826 0.3223392
## trend[167] trend[168] trend[169] trend[170] trend[171] trend[172]
## [1,] 0.3222959 0.3222525 0.3222092 0.3221659 0.3221225 0.3220792
## trend[173] trend[174] trend[175] trend[176] trend[177] trend[178]
## [1,] 0.3220359 0.3219925 0.3219492 0.3219058 0.3218625 0.3218192
## trend[179] trend[180] trend[181] trend[182] trend[183] trend[184]
## [1,] 0.3217758 0.3217325 0.3216892 0.3216458 0.3216025 0.3215592
## trend[185] trend[186] trend[187] trend[188] trend[189] trend[190]
## [1,] 0.3215158 0.3214725 0.3214291 0.3213858 0.3216663 0.3219468
## trend[191] trend[192] trend[193] trend[194] trend[195] trend[196]
## [1,] 0.3222272 0.3225077 0.3227882 0.3230687 0.3233491 0.3236296
## trend[197] trend[198] trend[199] trend[200] trend[201] trend[202]
## [1,] 0.3239101 0.3241906 0.324471 0.3247515 0.325032 0.3253125
## trend[203] trend[204] trend[205] trend[206] trend[207] trend[208]
## [1,] 0.3255929 0.3258734 0.3261539 0.3264343 0.3267148 0.3269953
## trend[209] trend[210] trend[211] trend[212] trend[213] trend[214]
## [1,] 0.3272758 0.3275562 0.3278367 0.3281172 0.3283977 0.3286781
## trend[215] trend[216] trend[217] trend[218] trend[219] trend[220]
## [1,] 0.3289586 0.3292391 0.3295196 0.3298 0.3300805 0.330361
## trend[221] trend[222] trend[223] trend[224] trend[225] trend[226]
## [1,] 0.3306415 0.3309219 0.3312024 0.3314829 0.3317634 0.3320438
## trend[227] trend[228] trend[229] trend[230] trend[231] trend[232]
## [1,] 0.3323243 0.3326048 0.3328853 0.3331657 0.3334462 0.3337267
## trend[233] trend[234] trend[235] trend[236] trend[237] trend[238]
## [1,] 0.3340072 0.3342876 0.3346995 0.3351114 0.3355233 0.3359351
## trend[239] trend[240] trend[241] trend[242] trend[243] trend[244]
## [1,] 0.336347 0.3367589 0.3371708 0.3375826 0.3379945 0.3384064
## trend[245] trend[246] trend[247] trend[248] trend[249] trend[250]
## [1,] 0.3388183 0.3392301 0.339642 0.3400539 0.3404658 0.3408776
## trend[251] trend[252] trend[253] trend[254] trend[255] trend[256]
## [1,] 0.3412895 0.3417014 0.3421133 0.3425251 0.342937 0.3433489
## trend[257] trend[258] trend[259] trend[260] trend[261] trend[262]
## [1,] 0.3437608 0.3441726 0.3445845 0.3449964 0.3454083 0.3458201
## trend[263] trend[264] trend[265] trend[266] trend[267] trend[268]
## [1,] 0.346232 0.3466439 0.3470558 0.3474677 0.3478795 0.3482914
## trend[269] trend[270] trend[271] trend[272] trend[273] trend[274]
## [1,] 0.3487033 0.3491152 0.349527 0.3499389 0.3503508 0.3507627
## trend[275] trend[276] trend[277] trend[278] trend[279] trend[280]
## [1,] 0.3511745 0.3515864 0.3519983 0.3524102 0.352822 0.3532339
## trend[281] trend[282] trend[283] trend[284] trend[285] trend[286]
## [1,] 0.3536458 0.3540577 0.3544695 0.3548814 0.3552933 0.3557052
## trend[287] trend[288] trend[289] trend[290] trend[291] trend[292]
## [1,] 0.356117 0.3565289 0.3569408 0.3573527 0.3577645 0.3581764
## trend[293] trend[294] trend[295] trend[296] trend[297] trend[298]
## [1,] 0.3585883 0.3590002 0.359412 0.3598239 0.3602358 0.3606477
## trend[299] trend[300] trend[301] trend[302] trend[303] trend[304]
## [1,] 0.3610595 0.3614714 0.3618833 0.3622952 0.362707 0.3631189
## trend[305] trend[306] trend[307] trend[308] trend[309] trend[310]
## [1,] 0.3635308 0.3639427 0.3643546 0.3647664 0.3651783 0.3655902
## trend[311] trend[312] trend[313] trend[314] trend[315] trend[316]
## [1,] 0.3660021 0.3664139 0.3668258 0.3672377 0.3676496 0.3680614
## trend[317] trend[318] trend[319] trend[320] trend[321] trend[322]
## [1,] 0.3684733 0.3688852 0.3692971 0.3697089 0.3701208 0.3705327
## trend[323] trend[324] trend[325] trend[326] trend[327] trend[328]
## [1,] 0.3709446 0.3713564 0.3717683 0.3721802 0.3725921 0.3730039
## trend[329] trend[330] trend[331] trend[332] trend[333] trend[334]
## [1,] 0.3734158 0.3738277 0.3742396 0.3746514 0.3750633 0.3754752
## trend[335] trend[336] trend[337] trend[338] trend[339] trend[340]
## [1,] 0.3758871 0.3762989 0.3767108 0.3771227 0.3775346 0.3779464
## trend[341] trend[342] trend[343] trend[344] trend[345] trend[346]
## [1,] 0.3783583 0.3787702 0.3791821 0.3795939 0.3800058 0.3804177
## trend[347] trend[348] trend[349] trend[350] trend[351] trend[352]
## [1,] 0.3808296 0.3812414 0.3816533 0.3820652 0.3824771 0.382889
## trend[353] trend[354] trend[355] trend[356] trend[357] trend[358]
## [1,] 0.3833008 0.3837127 0.3841246 0.3845365 0.3849483 0.3853602
## trend[359] trend[360] trend[361] trend[362] trend[363] trend[364]
## [1,] 0.3857721 0.386184 0.3865958 0.3870077 0.3874196 0.3878315
## trend[365] trend[366] trend[367] trend[368] trend[369] trend[370]
## [1,] 0.3882433 0.3886552 0.3890671 0.389479 0.3898908 0.3903027
## trend[371] trend[372] trend[373] trend[374] trend[375] trend[376]
## [1,] 0.3907146 0.3911265 0.3915383 0.3919502 0.3922193 0.3924883
## trend[377] trend[378] trend[379] trend[380] trend[381] trend[382]
## [1,] 0.3927574 0.3930265 0.3932955 0.3935646 0.3938336 0.3941027
## trend[383] trend[384] trend[385] trend[386] trend[387] trend[388]
## [1,] 0.3943718 0.3946408 0.3949099 0.3951789 0.395448 0.3957171
## trend[389] trend[390] trend[391] trend[392] trend[393] trend[394]
## [1,] 0.3959861 0.3962552 0.3965242 0.3967933 0.3970624 0.3973314
## trend[395] trend[396] trend[397] trend[398] trend[399] trend[400]
## [1,] 0.3976005 0.3978696 0.3981386 0.3984077 0.3986767 0.3989458
## trend[401] trend[402] trend[403] trend[404] trend[405] trend[406]
## [1,] 0.3992149 0.3994839 0.399753 0.400022 0.4002911 0.4005602
## trend[407] trend[408] trend[409] trend[410] trend[411] trend[412]
## [1,] 0.4008292 0.4010983 0.4013673 0.4016364 0.4019055 0.4021745
## trend[413] trend[414] trend[415] trend[416] trend[417] trend[418]
## [1,] 0.4024436 0.4027126 0.4029817 0.4032508 0.4035198 0.4037889
## trend[419] trend[420] trend[421] trend[422] trend[423] trend[424]
## [1,] 0.404058 0.404327 0.4045961 0.4046829 0.4047696 0.4048564
## trend[425] trend[426] trend[427] trend[428] trend[429] trend[430]
## [1,] 0.4049432 0.40503 0.4051167 0.4052035 0.4052903 0.4053771
## trend[431] trend[432] trend[433] trend[434] trend[435] trend[436]
## [1,] 0.4054638 0.4055506 0.4056374 0.4057242 0.405811 0.4058977
## trend[437] trend[438] trend[439] trend[440] trend[441] trend[442]
## [1,] 0.4059845 0.4060713 0.4061581 0.4062448 0.4063316 0.4064184
## trend[443] trend[444] trend[445] trend[446] trend[447] trend[448]
## [1,] 0.4065052 0.406592 0.4066787 0.4067655 0.4068523 0.4069391
## trend[449] trend[450] trend[451] trend[452] trend[453] trend[454]
## [1,] 0.4070258 0.4071126 0.4071994 0.4072862 0.407373 0.4074597
## trend[455] trend[456] trend[457] trend[458] trend[459] trend[460]
## [1,] 0.4075465 0.4076333 0.4077201 0.4078068 0.4078936 0.4079804
## trend[461] trend[462] trend[463] trend[464] trend[465] trend[466]
## [1,] 0.4080672 0.408154 0.4082407 0.4083275 0.4084143 0.4085011
## trend[467] trend[468] trend[469] trend[470] trend[471] trend[472]
## [1,] 0.4085878 0.4086746 0.4087614 0.4088482 0.408935 0.4090217
## trend[473] trend[474] trend[475] trend[476] trend[477] trend[478]
## [1,] 0.4091085 0.4091953 0.4092821 0.4093688 0.4094556 0.4095424
## trend[479] trend[480] trend[481] trend[482] trend[483] trend[484]
## [1,] 0.4096292 0.409716 0.4098027 0.4098895 0.4099763 0.4100631
## trend[485] trend[486] trend[487] trend[488] trend[489] trend[490]
## [1,] 0.4101498 0.4102366 0.4103234 0.4104102 0.410497 0.4105837
## trend[491] trend[492] trend[493] trend[494] trend[495] trend[496]
## [1,] 0.4106705 0.4107573 0.4108441 0.4109308 0.4110176 0.4111044
## trend[497] trend[498] trend[499] trend[500] trend[501] trend[502]
## [1,] 0.4111912 0.411278 0.4113647 0.4114515 0.4115383 0.4116251
## trend[503] trend[504] trend[505] trend[506] trend[507] trend[508]
## [1,] 0.4117118 0.4117986 0.4118854 0.4119722 0.412059 0.4121457
## trend[509] trend[510] trend[511] trend[512] trend[513] trend[514]
## [1,] 0.4122325 0.4123193 0.4124061 0.4124928 0.4125796 0.4126664
## trend[515] trend[516] trend[517] trend[518] trend[519] trend[520]
## [1,] 0.4127532 0.41284 0.4129267 0.4130135 0.4131003 0.4131871
## trend[521] trend[522] trend[523] trend[524] trend[525] trend[526]
## [1,] 0.4132738 0.4133606 0.4134474 0.4135342 0.413621 0.4137077
## trend[527] trend[528] trend[529] trend[530] trend[531] trend[532]
## [1,] 0.4137945 0.4138813 0.4139681 0.4140548 0.4141416 0.4142284
## trend[533] trend[534] trend[535] trend[536] trend[537] trend[538]
## [1,] 0.4143152 0.414402 0.4144887 0.4145755 0.4146623 0.4147491
## trend[539] trend[540] trend[541] trend[542] trend[543] trend[544]
## [1,] 0.4148358 0.4149226 0.4150094 0.4150962 0.415183 0.4152697
## trend[545] trend[546] trend[547] trend[548] trend[549] trend[550]
## [1,] 0.4153565 0.4154433 0.4155301 0.4156168 0.4157036 0.4157904
## trend[551] trend[552] trend[553] trend[554] trend[555] trend[556]
## [1,] 0.4158772 0.415964 0.4160507 0.4161375 0.4162243 0.4163111
## trend[557] trend[558] trend[559] trend[560] trend[561] trend[562]
## [1,] 0.4163978 0.4164846 0.4165714 0.4166582 0.416745 0.4168317
## trend[563] trend[564] trend[565] trend[566] trend[567] trend[568]
## [1,] 0.4169185 0.4170053 0.4170921 0.4171788 0.4172656 0.4173524
## trend[569] trend[570] trend[571] trend[572] trend[573] trend[574]
## [1,] 0.4174392 0.417526 0.4176127 0.4176995 0.4177863 0.4178731
## trend[575] trend[576] trend[577] trend[578] trend[579] trend[580]
## [1,] 0.4179598 0.4180466 0.4181334 0.4182202 0.418307 0.4183937
## trend[581] trend[582] trend[583] trend[584] trend[585] trend[586]
## [1,] 0.4184805 0.4185673 0.4186541 0.4187408 0.4188276 0.4189144
## trend[587] trend[588] trend[589] trend[590] trend[591] trend[592]
## [1,] 0.4190012 0.419088 0.4191747 0.4192615 0.4193483 0.4194351
## trend[593] trend[594] trend[595] trend[596] trend[597] trend[598]
## [1,] 0.4195218 0.4196086 0.4196954 0.4197822 0.419869 0.4199557
## trend[599] trend[600] trend[601] trend[602] trend[603] trend[604]
## [1,] 0.4200425 0.4201293 0.4202161 0.4203028 0.4203896 0.4204764
## trend[605] trend[606] trend[607] trend[608] trend[609] trend[610]
## [1,] 0.4205632 0.42065 0.4207367 0.4208235 0.4209103 0.4209971
## trend[611] trend[612] trend[613] trend[614] trend[615] trend[616]
## [1,] 0.4210838 0.4211706 0.4212574 0.4213442 0.421431 0.4215177
## trend[617] trend[618] trend[619] trend[620] trend[621] trend[622]
## [1,] 0.4216045 0.4216913 0.4217781 0.4218648 0.4219516 0.4220384
## trend[623] trend[624] trend[625] trend[626] trend[627] trend[628]
## [1,] 0.4221252 0.422212 0.4222987 0.4223855 0.4224723 0.4225591
## trend[629] trend[630] trend[631] trend[632] trend[633] trend[634]
## [1,] 0.4226458 0.4227326 0.4228194 0.4229062 0.422993 0.4230797
## trend[635] trend[636] trend[637] trend[638] trend[639] trend[640]
## [1,] 0.4231665 0.4232533 0.4233401 0.4234268 0.4235136 0.4236004
## trend[641] trend[642] trend[643] trend[644] trend[645] trend[646]
## [1,] 0.4236872 0.423774 0.4238607 0.4239475 0.4240343 0.4241211
## trend[647] trend[648] trend[649] trend[650] trend[651] trend[652]
## [1,] 0.4242078 0.4242946 0.4243814 0.4244682 0.424555 0.4246417
## trend[653] trend[654] trend[655] trend[656] trend[657] trend[658]
## [1,] 0.4247285 0.4248153 0.4249021 0.424981 0.42506 0.425139
## trend[659] trend[660] trend[661] trend[662] trend[663] trend[664]
## [1,] 0.4252179 0.4252969 0.4253759 0.4254548 0.4255338 0.4256128
## trend[665] trend[666] trend[667] trend[668] trend[669] trend[670]
## [1,] 0.4256917 0.4257707 0.4258497 0.4259286 0.4260076 0.4260866
## trend[671] trend[672] trend[673] trend[674] trend[675] trend[676]
## [1,] 0.4261655 0.4262445 0.4263235 0.4264024 0.4264814 0.4265604
## trend[677] trend[678] trend[679] trend[680] trend[681] trend[682]
## [1,] 0.4266393 0.4267183 0.4267973 0.4268762 0.4269552 0.4270342
## trend[683] trend[684] trend[685] trend[686] trend[687] trend[688]
## [1,] 0.4271131 0.4271921 0.4272711 0.42735 0.427429 0.427508
## trend[689] trend[690] trend[691] trend[692] trend[693] trend[694]
## [1,] 0.4275869 0.4276659 0.4277449 0.4278238 0.4279028 0.4279818
## trend[695] trend[696] trend[697] trend[698] trend[699] trend[700]
## [1,] 0.4280607 0.4281397 0.4282187 0.4282976 0.4283766 0.4284555
## trend[701] trend[702] trend[703] trend[704] trend[705] trend[706]
## [1,] 0.4285345 0.4285939 0.4286534 0.4287128 0.4287722 0.4288316
## trend[707] trend[708] trend[709] trend[710] trend[711] trend[712]
## [1,] 0.4288911 0.4289505 0.4290099 0.4290693 0.4291287 0.4291882
## trend[713] trend[714] trend[715] trend[716] trend[717] trend[718]
## [1,] 0.4292476 0.429307 0.4293664 0.4294259 0.4294853 0.4295447
## trend[719] trend[720] trend[721] trend[722] trend[723] trend[724]
## [1,] 0.4296041 0.4296635 0.429723 0.4297824 0.4298418 0.4299012
## trend[725] trend[726] trend[727] trend[728] trend[729] trend[730]
## [1,] 0.4299607 0.4300201 0.4300795 0.4301389 0.4301984 0.4302578
## trend[731] trend[732] trend[733] trend[734] trend[735] trend[736]
## [1,] 0.4303172 0.4303766 0.430436 0.4304955 0.4305549 0.4306143
## trend[737] trend[738] trend[739] trend[740] trend[741] trend[742]
## [1,] 0.4306737 0.4307332 0.4307926 0.430852 0.4309114 0.4309708
## trend[743] trend[744] trend[745] trend[746] trend[747] trend[748]
## [1,] 0.4310303 0.4310897 0.4311491 0.4312085 0.431268 0.4313274
## trend[749] trend[750] trend[751] trend[752] trend[753] trend[754]
## [1,] 0.4313868 0.4314462 0.4315057 0.4315651 0.4316245 0.4316839
## trend[755] trend[756] trend[757] trend[758] trend[759] trend[760]
## [1,] 0.4317433 0.4318028 0.4318622 0.4319216 0.431981 0.4320405
## trend[761] trend[762] trend[763] trend[764] trend[765] trend[766]
## [1,] 0.4320999 0.4321593 0.4322187 0.4322781 0.4323376 0.432397
## trend[767] trend[768] trend[769] trend[770] trend[771] trend[772]
## [1,] 0.4324564 0.4325158 0.4325753 0.4326347 0.4326941 0.4327535
## trend[773] trend[774] trend[775] trend[776] trend[777] trend[778]
## [1,] 0.432813 0.4328724 0.4329318 0.4329912 0.4330506 0.4331101
## trend[779] trend[780] trend[781] trend[782] trend[783] trend[784]
## [1,] 0.4331695 0.4332289 0.4332883 0.4333478 0.4334072 0.4334666
## trend[785] trend[786] trend[787] trend[788] trend[789] trend[790]
## [1,] 0.433526 0.4335855 0.4336449 0.4337043 0.4337637 0.4338231
## trend[791] trend[792] trend[793] trend[794] trend[795] trend[796]
## [1,] 0.4338826 0.433942 0.4340014 0.4340608 0.4341203 0.4341797
## trend[797] trend[798] trend[799] trend[800] trend[801] trend[802]
## [1,] 0.4342391 0.4342985 0.4343579 0.4344174 0.4344768 0.4345362
## trend[803] trend[804] trend[805] trend[806] trend[807] trend[808]
## [1,] 0.4345956 0.4346551 0.4347145 0.4347739 0.4348333 0.4348928
## trend[809] trend[810] trend[811] trend[812] trend[813] trend[814]
## [1,] 0.4349522 0.4350116 0.435071 0.4351304 0.4351899 0.4352493
## trend[815] trend[816] trend[817] trend[818] trend[819] trend[820]
## [1,] 0.4353087 0.4353681 0.4354276 0.435487 0.4355464 0.4356058
## trend[821] trend[822] trend[823] trend[824] trend[825] trend[826]
## [1,] 0.4356653 0.4357247 0.4357841 0.4358435 0.4359029 0.4359624
## trend[827] trend[828] trend[829] trend[830] trend[831] trend[832]
## [1,] 0.4360218 0.4360812 0.4361406 0.4362001 0.4362595 0.4363189
## trend[833] trend[834] trend[835] trend[836] trend[837] trend[838]
## [1,] 0.4363783 0.4364377 0.4364972 0.4365566 0.436616 0.4366754
## trend[839] trend[840] trend[841] trend[842] trend[843] trend[844]
## [1,] 0.4367349 0.4367943 0.4368537 0.4369184 0.4369831 0.4370478
## trend[845] trend[846] trend[847] trend[848] trend[849] trend[850]
## [1,] 0.4371125 0.4371772 0.4372419 0.4373066 0.4373713 0.437436
## trend[851] trend[852] trend[853] trend[854] trend[855] trend[856]
## [1,] 0.4375007 0.4375654 0.4376301 0.4376948 0.4377595 0.4378242
## trend[857] trend[858] trend[859] trend[860] trend[861] trend[862]
## [1,] 0.4378888 0.4379535 0.4380182 0.4380829 0.4381476 0.4382123
## trend[863] trend[864] trend[865] trend[866] trend[867] trend[868]
## [1,] 0.438277 0.4383417 0.4384064 0.4384711 0.4385358 0.4386005
## trend[869] trend[870] trend[871] trend[872] trend[873] trend[874]
## [1,] 0.4386652 0.4387299 0.4387946 0.4388593 0.438924 0.4389887
## trend[875] trend[876] trend[877] trend[878] trend[879] trend[880]
## [1,] 0.4390534 0.4391181 0.4391828 0.4392475 0.4393122 0.4393769
## trend[881] trend[882] trend[883] trend[884] trend[885] trend[886]
## [1,] 0.4394416 0.4395063 0.4395709 0.4396356 0.4397003 0.439765
## trend[887] trend[888] trend[889] trend[890] trend[891] trend[892]
## [1,] 0.4398297 0.4398944 0.4399615 0.4400286 0.4400956 0.4401627
## trend[893] trend[894] trend[895] trend[896] trend[897] trend[898]
## [1,] 0.4402298 0.4402969 0.4403639 0.440431 0.4404981 0.4405652
## trend[899] trend[900] trend[901] trend[902] trend[903] trend[904]
## [1,] 0.4406322 0.4406993 0.4407664 0.4408335 0.4409005 0.4409676
## trend[905] trend[906] trend[907] trend[908] trend[909] trend[910]
## [1,] 0.4410347 0.4411018 0.4411688 0.4412359 0.441303 0.44137
## trend[911] trend[912] trend[913] trend[914] trend[915] trend[916]
## [1,] 0.4414371 0.4415042 0.4415713 0.4416383 0.4417054 0.4417725
## trend[917] trend[918] trend[919] trend[920] trend[921] trend[922]
## [1,] 0.4418396 0.4419066 0.4419737 0.4420408 0.4421079 0.4421749
## trend[923] trend[924] trend[925] trend[926] trend[927] trend[928]
## [1,] 0.442242 0.4423091 0.4423761 0.4424432 0.4425103 0.4425774
## trend[929] trend[930] trend[931] trend[932] trend[933] trend[934]
## [1,] 0.4426444 0.4427115 0.4427786 0.4428457 0.4429127 0.4429798
## trend[935] trend[936] trend[937] trend[938] trend[939] trend[940]
## [1,] 0.4430469 0.443147 0.4432471 0.4433472 0.4434473 0.4435474
## trend[941] trend[942] trend[943] trend[944] trend[945] trend[946]
## [1,] 0.4436476 0.4437477 0.4438478 0.4439479 0.444048 0.4441481
## trend[947] trend[948] trend[949] trend[950] trend[951] trend[952]
## [1,] 0.4442482 0.4443483 0.4444484 0.4445486 0.4446487 0.4447488
## trend[953] trend[954] trend[955] trend[956] trend[957] trend[958]
## [1,] 0.4448489 0.444949 0.4450491 0.4451492 0.4452493 0.4453494
## trend[959] trend[960] trend[961] trend[962] trend[963] trend[964]
## [1,] 0.4454496 0.4455497 0.4456498 0.4457499 0.44585 0.4459501
## trend[965] trend[966] trend[967] trend[968] trend[969] trend[970]
## [1,] 0.4460502 0.4461503 0.4462504 0.4463505 0.4464507 0.4465508
## trend[971] trend[972] trend[973] trend[974] trend[975] trend[976]
## [1,] 0.4466509 0.446751 0.4468511 0.4469512 0.4470513 0.4471514
## trend[977] trend[978] trend[979] trend[980] trend[981] trend[982]
## [1,] 0.4472515 0.4473517 0.4474518 0.4475519 0.447652 0.4478047
## trend[983] trend[984] trend[985] trend[986] trend[987] trend[988]
## [1,] 0.4479574 0.4481101 0.4482628 0.4484155 0.4485682 0.448721
## trend[989] trend[990] trend[991] trend[992] trend[993] trend[994]
## [1,] 0.4488737 0.4490264 0.4491791 0.4493318 0.4494845 0.4496372
## trend[995] trend[996] trend[997] trend[998] trend[999] trend[1000]
## [1,] 0.4497899 0.4499426 0.4500953 0.450248 0.4504008 0.4505535
## trend[1001] trend[1002] trend[1003] trend[1004] trend[1005] trend[1006]
## [1,] 0.4507062 0.4508589 0.4510116 0.4511643 0.451317 0.4514697
## trend[1007] trend[1008] trend[1009] trend[1010] trend[1011] trend[1012]
## [1,] 0.4516224 0.4517751 0.4519278 0.4520806 0.4522333 0.452386
## trend[1013] trend[1014] trend[1015] trend[1016] trend[1017] trend[1018]
## [1,] 0.4525387 0.4526914 0.4528441 0.4529968 0.4531495 0.4533022
## trend[1019] trend[1020] trend[1021] trend[1022] trend[1023] trend[1024]
## [1,] 0.4534549 0.4536076 0.4537604 0.4539131 0.4540658 0.4542185
## trend[1025] trend[1026] trend[1027] trend[1028] trend[1029] trend[1030]
## [1,] 0.4543712 0.4545239 0.4546766 0.4548293 0.4549993 0.4551693
## trend[1031] trend[1032] trend[1033] trend[1034] trend[1035] trend[1036]
## [1,] 0.4553393 0.4555093 0.4556793 0.4558492 0.4560192 0.4561892
## trend[1037] trend[1038] trend[1039] trend[1040] trend[1041] trend[1042]
## [1,] 0.4563592 0.4565292 0.4566992 0.4568692 0.4570391 0.4572091
## trend[1043] trend[1044] trend[1045] trend[1046] trend[1047] trend[1048]
## [1,] 0.4573791 0.4575491 0.4577191 0.4578891 0.4580591 0.4582291
## trend[1049] trend[1050] trend[1051] trend[1052] trend[1053] trend[1054]
## [1,] 0.458399 0.458569 0.458739 0.458909 0.459079 0.459249
## trend[1055] trend[1056] trend[1057] trend[1058] trend[1059] trend[1060]
## [1,] 0.459419 0.4595889 0.4597589 0.4599289 0.4600989 0.4602689
## trend[1061] trend[1062] trend[1063] trend[1064] trend[1065] trend[1066]
## [1,] 0.4604389 0.4606089 0.4607789 0.4609488 0.4611188 0.4612888
## trend[1067] trend[1068] trend[1069] trend[1070] trend[1071] trend[1072]
## [1,] 0.4614588 0.4616288 0.4617988 0.4619688 0.4621387 0.4623087
## trend[1073] trend[1074] trend[1075] trend[1076] trend[1077] trend[1078]
## [1,] 0.4624787 0.4626487 0.4628187 0.4629887 0.4631587 0.4633287
## trend[1079] trend[1080] trend[1081] trend[1082] trend[1083] trend[1084]
## [1,] 0.4634986 0.4636686 0.4638386 0.4640086 0.4641786 0.4643486
## trend[1085] trend[1086] trend[1087] trend[1088] trend[1089] trend[1090]
## [1,] 0.4645186 0.4646885 0.4648585 0.4650285 0.4651985 0.4653685
## trend[1091] trend[1092] trend[1093] trend[1094] trend[1095] trend[1096]
## [1,] 0.4655385 0.4657085 0.4658785 0.4660484 0.4662184 0.4663884
## trend[1097] trend[1098] trend[1099] trend[1100] trend[1101] trend[1102]
## [1,] 0.4665584 0.4667284 0.4668984 0.4670684 0.4672383 0.4674083
## trend[1103] trend[1104] trend[1105] trend[1106] trend[1107] trend[1108]
## [1,] 0.4675783 0.4677483 0.4679183 0.4680883 0.4682583 0.4684283
## trend[1109] trend[1110] trend[1111] trend[1112] trend[1113] trend[1114]
## [1,] 0.4685982 0.4687682 0.4689382 0.4691082 0.4692782 0.4694482
## trend[1115] trend[1116] trend[1117] trend[1118] trend[1119] trend[1120]
## [1,] 0.4696182 0.4697881 0.4699581 0.4701281 0.4702981 0.4704681
## trend[1121] trend[1122] trend[1123] trend[1124] trend[1125] trend[1126]
## [1,] 0.4706381 0.4708081 0.4709781 0.471148 0.471318 0.471488
## trend[1127] trend[1128] trend[1129] trend[1130] trend[1131] trend[1132]
## [1,] 0.471658 0.471828 0.471998 0.472168 0.4723379 0.4725079
## trend[1133] trend[1134] trend[1135] trend[1136] trend[1137] trend[1138]
## [1,] 0.4726779 0.4728479 0.4730179 0.4731879 0.4733579 0.4735279
## trend[1139] trend[1140] trend[1141] trend[1142] trend[1143] trend[1144]
## [1,] 0.4736978 0.4738678 0.4740378 0.4742078 0.4743778 0.4745478
## trend[1145] trend[1146] trend[1147] trend[1148] trend[1149] trend[1150]
## [1,] 0.4747178 0.4748877 0.4750577 0.4752277 0.4753977 0.4755677
## trend[1151] trend[1152] trend[1153] trend[1154] trend[1155] trend[1156]
## [1,] 0.4757377 0.4759077 0.4760777 0.4762476 0.4764176 0.4765876
## trend[1157] trend[1158] trend[1159] trend[1160] trend[1161] trend[1162]
## [1,] 0.4767576 0.4769276 0.4770976 0.4772676 0.4774375 0.4776075
## trend[1163] trend[1164] trend[1165] trend[1166] trend[1167] trend[1168]
## [1,] 0.4777775 0.4779475 0.4781175 0.4782875 0.4784575 0.4786275
## trend[1169] trend[1170] trend[1171] trend[1172] trend[1173] trend[1174]
## [1,] 0.478753 0.4788785 0.4790041 0.4791296 0.4792551 0.4793807
## trend[1175] trend[1176] trend[1177] trend[1178] trend[1179] trend[1180]
## [1,] 0.4795062 0.4796317 0.4797573 0.4798828 0.4800084 0.4801339
## trend[1181] trend[1182] trend[1183] trend[1184] trend[1185] trend[1186]
## [1,] 0.4802594 0.480385 0.4805105 0.480636 0.4807616 0.4808871
## trend[1187] trend[1188] trend[1189] trend[1190] trend[1191] trend[1192]
## [1,] 0.4810126 0.4811382 0.4812637 0.4813892 0.4815148 0.4816403
## trend[1193] trend[1194] trend[1195] trend[1196] trend[1197] trend[1198]
## [1,] 0.4817659 0.4818914 0.4820169 0.4821425 0.482268 0.4823935
## trend[1199] trend[1200] trend[1201] trend[1202] trend[1203] trend[1204]
## [1,] 0.4825191 0.4826446 0.4827701 0.4828957 0.4830212 0.4831468
## trend[1205] trend[1206] trend[1207] trend[1208] trend[1209] trend[1210]
## [1,] 0.4832723 0.4833978 0.4835234 0.4836489 0.4837744 0.4839
## trend[1211] trend[1212] trend[1213] trend[1214] trend[1215] trend[1216]
## [1,] 0.4840255 0.484151 0.4842766 0.4844021 0.4845277 0.4846532
## trend[1217] trend[1218] trend[1219] trend[1220] trend[1221] trend[1222]
## [1,] 0.4847787 0.4849043 0.4850298 0.4851553 0.4852809 0.4854064
## trend[1223] trend[1224] trend[1225] trend[1226] trend[1227] trend[1228]
## [1,] 0.4855319 0.4856575 0.485783 0.4859086 0.4860341 0.4861596
## trend[1229] trend[1230] trend[1231] trend[1232] trend[1233] trend[1234]
## [1,] 0.4862852 0.4864107 0.4865362 0.4866618 0.4867873 0.4869128
## trend[1235] trend[1236] trend[1237] trend[1238] trend[1239] trend[1240]
## [1,] 0.4870384 0.4871639 0.4872894 0.487415 0.4875405 0.4876661
## trend[1241] trend[1242] trend[1243] trend[1244] trend[1245] trend[1246]
## [1,] 0.4877916 0.4879171 0.4880427 0.4881682 0.4882937 0.4884193
## trend[1247] trend[1248] trend[1249] trend[1250] trend[1251] trend[1252]
## [1,] 0.4885448 0.4886703 0.4887959 0.4889214 0.489047 0.4891725
## trend[1253] trend[1254] trend[1255] trend[1256] trend[1257] trend[1258]
## [1,] 0.489298 0.4894236 0.4895491 0.4896746 0.4898002 0.4899257
## trend[1259] trend[1260] trend[1261] trend[1262] trend[1263] trend[1264]
## [1,] 0.4900512 0.4901768 0.4903023 0.4904279 0.4905534 0.4906789
## trend[1265] trend[1266] trend[1267] trend[1268] trend[1269] trend[1270]
## [1,] 0.4908045 0.49093 0.4910555 0.4911811 0.4913066 0.4914321
## trend[1271] trend[1272] trend[1273] trend[1274] trend[1275] trend[1276]
## [1,] 0.4915577 0.4916832 0.4918088 0.4919343 0.4920598 0.4921854
## trend[1277] trend[1278] trend[1279] trend[1280] trend[1281] trend[1282]
## [1,] 0.4923109 0.4924364 0.492562 0.4926875 0.492813 0.4929386
## trend[1283] trend[1284] trend[1285] trend[1286] trend[1287] trend[1288]
## [1,] 0.4930641 0.4931896 0.4933152 0.4934407 0.4935663 0.4936918
## trend[1289] trend[1290] trend[1291] trend[1292] trend[1293] trend[1294]
## [1,] 0.4938173 0.4939429 0.4940684 0.4941939 0.4943195 0.494445
## trend[1295] trend[1296] trend[1297] trend[1298] trend[1299] trend[1300]
## [1,] 0.4945705 0.4946961 0.4948216 0.4949472 0.4950727 0.4951982
## trend[1301] trend[1302] trend[1303] trend[1304] trend[1305] trend[1306]
## [1,] 0.4953238 0.4954493 0.4955748 0.4957004 0.4958259 0.4959514
## trend[1307] trend[1308] trend[1309] trend[1310] trend[1311] trend[1312]
## [1,] 0.496077 0.4962025 0.4963281 0.4964536 0.4965791 0.4967047
## trend[1313] trend[1314] trend[1315] trend[1316] trend[1317] trend[1318]
## [1,] 0.4968302 0.4969557 0.4970813 0.4972068 0.4973323 0.4974579
## trend[1319] trend[1320] trend[1321] trend[1322] trend[1323] trend[1324]
## [1,] 0.4975834 0.497709 0.4978345 0.49796 0.4980856 0.4982111
## trend[1325] trend[1326] trend[1327] trend[1328] trend[1329] trend[1330]
## [1,] 0.4983366 0.4984622 0.4985877 0.4987132 0.4988388 0.4989643
## trend[1331] trend[1332] trend[1333] trend[1334] trend[1335] trend[1336]
## [1,] 0.4990898 0.4992154 0.4993409 0.4994665 0.499592 0.4997175
## trend[1337] trend[1338] trend[1339] trend[1340] trend[1341] trend[1342]
## [1,] 0.4998431 0.4999686 0.5000941 0.5002197 0.5003452 0.5004707
## trend[1343] trend[1344] trend[1345] trend[1346] trend[1347] trend[1348]
## [1,] 0.5005963 0.5007218 0.5008474 0.5009729 0.5010984 0.501224
## trend[1349] trend[1350] trend[1351] trend[1352] trend[1353] trend[1354]
## [1,] 0.5013495 0.501475 0.5016006 0.5017261 0.5018516 0.5019772
## trend[1355] trend[1356] trend[1357] trend[1358] trend[1359] trend[1360]
## [1,] 0.5021027 0.5022283 0.5023538 0.5024793 0.5026049 0.5027304
## trend[1361] trend[1362] trend[1363] trend[1364] trend[1365] trend[1366]
## [1,] 0.5028559 0.5029815 0.503107 0.5032325 0.5033581 0.5034836
## trend[1367] trend[1368] trend[1369] trend[1370] trend[1371] trend[1372]
## [1,] 0.5036092 0.5037347 0.5038602 0.5039858 0.5041113 0.5042368
## trend[1373] trend[1374] trend[1375] trend[1376] trend[1377] trend[1378]
## [1,] 0.5043624 0.5044879 0.5046134 0.504739 0.5048645 0.50499
## trend[1379] trend[1380] trend[1381] trend[1382] trend[1383] trend[1384]
## [1,] 0.5051156 0.5052411 0.5053667 0.5054922 0.5056177 0.5057433
## trend[1385] trend[1386] trend[1387] trend[1388] trend[1389] trend[1390]
## [1,] 0.5058688 0.5059943 0.5061199 0.5062454 0.5063709 0.5064965
## trend[1391] trend[1392] trend[1393] trend[1394] trend[1395] trend[1396]
## [1,] 0.506622 0.5067476 0.5068731 0.5069986 0.5071242 0.5072497
## trend[1397] trend[1398] trend[1399] trend[1400] trend[1401] trend[1402]
## [1,] 0.5073752 0.5075008 0.5076263 0.5077518 0.5078774 0.5080029
## trend[1403] trend[1404] trend[1405] trend[1406] trend[1407] trend[1408]
## [1,] 0.5081285 0.508254 0.5083795 0.5085051 0.5086306 0.5087561
## trend[1409] trend[1410] trend[1411] trend[1412] trend[1413] trend[1414]
## [1,] 0.5088817 0.5090072 0.5091327 0.5092583 0.5093838 0.5095094
## trend[1415] trend[1416] trend[1417] trend[1418] trend[1419] trend[1420]
## [1,] 0.5096349 0.5097604 0.509886 0.5100115 0.510137 0.5102626
## trend[1421] trend[1422] trend[1423] trend[1424] trend[1425] trend[1426]
## [1,] 0.5103881 0.5105136 0.5106392 0.5107647 0.5108902 0.5110158
## trend[1427] trend[1428] trend[1429] trend[1430] trend[1431] trend[1432]
## [1,] 0.5111413 0.5112669 0.5113924 0.5115179 0.5116435 0.511769
## trend[1433] trend[1434] trend[1435] trend[1436] trend[1437] trend[1438]
## [1,] 0.5118945 0.5120201 0.5121456 0.5122711 0.5123967 0.5125222
## trend[1439] trend[1440] trend[1441] trend[1442] trend[1443] trend[1444]
## [1,] 0.5126478 0.5127733 0.5128988 0.5130244 0.5131499 0.5132754
## trend[1445] trend[1446] trend[1447] trend[1448] trend[1449] trend[1450]
## [1,] 0.513401 0.5135265 0.513652 0.5137776 0.5139031 0.5140287
## trend[1451] trend[1452] trend[1453] trend[1454] trend[1455] trend[1456]
## [1,] 0.5141542 0.5142797 0.5144053 0.5145308 0.5146563 0.5147819
## trend[1457] trend[1458] trend[1459] trend[1460] trend[1461]
## [1,] 0.5149074 0.5150329 0.5151585 0.515284 0.5154095
##
##
## $params
## $params$k
## [1] -0.3295687
##
## $params$m
## [1] 0.3550251
##
## $params$delta
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.256203e-07 -2.981828e-08 0.2662971 0.4727642 0.1918457 -1.123155e-07
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 5.084654e-08 -0.2085096 -0.2661333 2.654932e-08 -3.862036e-09 1.096295e-07
## [,13] [,14] [,15] [,16] [,17]
## [1,] -4.993257e-09 -0.01140498 -0.02853337 -2.476382e-08 1.702067e-07
## [,18] [,19] [,20] [,21] [,22] [,23]
## [1,] 0.007699039 0.003470921 0.04823478 0.07679313 0.0252252 3.485977e-08
## [,24] [,25]
## [1,] 3.816875e-08 -0.06489775
##
## $params$sigma_obs
## [1] 0.02706113
##
## $params$beta
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.01495432 -0.1393878 -0.02409588 -0.007911498 -0.01775391 -0.02432144
## [,7] [,8] [,9] [,10] [,11] [,12]
## [1,] 0.007720784 -0.008146249 0.006691417 -0.01189065 0.01537089 0.003035046
## [,13] [,14] [,15] [,16] [,17] [,18]
## [1,] 0.003266428 0.009648419 0.004178968 0.005075157 -0.007409245 0.005949041
## [,19] [,20] [,21] [,22] [,23] [,24]
## [1,] -0.004866335 -0.000455657 0.07696754 -0.002570954 -0.04462192 -0.009995636
## [,25] [,26] [,27] [,28] [,29] [,30]
## [1,] 0.04729545 0.006687884 -5.301163e-11 0.03808422 -1.060233e-10 0.03808422
## [,31] [,32] [,33] [,34]
## [1,] -2.660458e-11 0.03808422 -2.120465e-10 0.03808422
##
## $params$trend
## [1] 0.3550251 0.3547994 0.3545736 0.3543479 0.3541222 0.3538964 0.3536707
## [8] 0.3534450 0.3532192 0.3529935 0.3527678 0.3525420 0.3523163 0.3520906
## [15] 0.3518649 0.3516391 0.3514134 0.3511877 0.3509619 0.3507362 0.3505105
## [22] 0.3502847 0.3500590 0.3498333 0.3496075 0.3493818 0.3491561 0.3489303
## [29] 0.3487046 0.3484789 0.3482531 0.3480274 0.3478017 0.3475759 0.3473502
## [36] 0.3471245 0.3468987 0.3466730 0.3464473 0.3462216 0.3459958 0.3457701
## [43] 0.3455444 0.3453186 0.3450929 0.3448672 0.3446414 0.3444157 0.3441900
## [50] 0.3439642 0.3437385 0.3435128 0.3432870 0.3430613 0.3428356 0.3426098
## [57] 0.3423841 0.3421584 0.3419326 0.3417069 0.3414812 0.3412555 0.3410297
## [64] 0.3408040 0.3405783 0.3403525 0.3401268 0.3399011 0.3396753 0.3394496
## [71] 0.3392239 0.3389981 0.3387724 0.3385467 0.3383209 0.3380952 0.3378695
## [78] 0.3376437 0.3374180 0.3371923 0.3369665 0.3367408 0.3365151 0.3362893
## [85] 0.3360636 0.3358379 0.3356122 0.3353864 0.3351607 0.3349350 0.3347092
## [92] 0.3344835 0.3342578 0.3340320 0.3338063 0.3335806 0.3333548 0.3331291
## [99] 0.3329034 0.3326776 0.3324519 0.3322262 0.3320004 0.3317747 0.3315490
## [106] 0.3313232 0.3310975 0.3308718 0.3306461 0.3304203 0.3301946 0.3299689
## [113] 0.3297431 0.3295174 0.3292917 0.3290659 0.3288402 0.3286145 0.3283887
## [120] 0.3281630 0.3279373 0.3277115 0.3274858 0.3272601 0.3270343 0.3268086
## [127] 0.3265829 0.3263571 0.3261314 0.3259057 0.3256799 0.3254542 0.3252285
## [134] 0.3250028 0.3247770 0.3245513 0.3243256 0.3240998 0.3238741 0.3236484
## [141] 0.3234226 0.3233793 0.3233360 0.3232926 0.3232493 0.3232059 0.3231626
## [148] 0.3231193 0.3230759 0.3230326 0.3229893 0.3229459 0.3229026 0.3228593
## [155] 0.3228159 0.3227726 0.3227292 0.3226859 0.3226426 0.3225992 0.3225559
## [162] 0.3225126 0.3224692 0.3224259 0.3223826 0.3223392 0.3222959 0.3222525
## [169] 0.3222092 0.3221659 0.3221225 0.3220792 0.3220359 0.3219925 0.3219492
## [176] 0.3219058 0.3218625 0.3218192 0.3217758 0.3217325 0.3216892 0.3216458
## [183] 0.3216025 0.3215592 0.3215158 0.3214725 0.3214291 0.3213858 0.3216663
## [190] 0.3219468 0.3222272 0.3225077 0.3227882 0.3230687 0.3233491 0.3236296
## [197] 0.3239101 0.3241906 0.3244710 0.3247515 0.3250320 0.3253125 0.3255929
## [204] 0.3258734 0.3261539 0.3264343 0.3267148 0.3269953 0.3272758 0.3275562
## [211] 0.3278367 0.3281172 0.3283977 0.3286781 0.3289586 0.3292391 0.3295196
## [218] 0.3298000 0.3300805 0.3303610 0.3306415 0.3309219 0.3312024 0.3314829
## [225] 0.3317634 0.3320438 0.3323243 0.3326048 0.3328853 0.3331657 0.3334462
## [232] 0.3337267 0.3340072 0.3342876 0.3346995 0.3351114 0.3355233 0.3359351
## [239] 0.3363470 0.3367589 0.3371708 0.3375826 0.3379945 0.3384064 0.3388183
## [246] 0.3392301 0.3396420 0.3400539 0.3404658 0.3408776 0.3412895 0.3417014
## [253] 0.3421133 0.3425251 0.3429370 0.3433489 0.3437608 0.3441726 0.3445845
## [260] 0.3449964 0.3454083 0.3458201 0.3462320 0.3466439 0.3470558 0.3474677
## [267] 0.3478795 0.3482914 0.3487033 0.3491152 0.3495270 0.3499389 0.3503508
## [274] 0.3507627 0.3511745 0.3515864 0.3519983 0.3524102 0.3528220 0.3532339
## [281] 0.3536458 0.3540577 0.3544695 0.3548814 0.3552933 0.3557052 0.3561170
## [288] 0.3565289 0.3569408 0.3573527 0.3577645 0.3581764 0.3585883 0.3590002
## [295] 0.3594120 0.3598239 0.3602358 0.3606477 0.3610595 0.3614714 0.3618833
## [302] 0.3622952 0.3627070 0.3631189 0.3635308 0.3639427 0.3643546 0.3647664
## [309] 0.3651783 0.3655902 0.3660021 0.3664139 0.3668258 0.3672377 0.3676496
## [316] 0.3680614 0.3684733 0.3688852 0.3692971 0.3697089 0.3701208 0.3705327
## [323] 0.3709446 0.3713564 0.3717683 0.3721802 0.3725921 0.3730039 0.3734158
## [330] 0.3738277 0.3742396 0.3746514 0.3750633 0.3754752 0.3758871 0.3762989
## [337] 0.3767108 0.3771227 0.3775346 0.3779464 0.3783583 0.3787702 0.3791821
## [344] 0.3795939 0.3800058 0.3804177 0.3808296 0.3812414 0.3816533 0.3820652
## [351] 0.3824771 0.3828890 0.3833008 0.3837127 0.3841246 0.3845365 0.3849483
## [358] 0.3853602 0.3857721 0.3861840 0.3865958 0.3870077 0.3874196 0.3878315
## [365] 0.3882433 0.3886552 0.3890671 0.3894790 0.3898908 0.3903027 0.3907146
## [372] 0.3911265 0.3915383 0.3919502 0.3922193 0.3924883 0.3927574 0.3930265
## [379] 0.3932955 0.3935646 0.3938336 0.3941027 0.3943718 0.3946408 0.3949099
## [386] 0.3951789 0.3954480 0.3957171 0.3959861 0.3962552 0.3965242 0.3967933
## [393] 0.3970624 0.3973314 0.3976005 0.3978696 0.3981386 0.3984077 0.3986767
## [400] 0.3989458 0.3992149 0.3994839 0.3997530 0.4000220 0.4002911 0.4005602
## [407] 0.4008292 0.4010983 0.4013673 0.4016364 0.4019055 0.4021745 0.4024436
## [414] 0.4027126 0.4029817 0.4032508 0.4035198 0.4037889 0.4040580 0.4043270
## [421] 0.4045961 0.4046829 0.4047696 0.4048564 0.4049432 0.4050300 0.4051167
## [428] 0.4052035 0.4052903 0.4053771 0.4054638 0.4055506 0.4056374 0.4057242
## [435] 0.4058110 0.4058977 0.4059845 0.4060713 0.4061581 0.4062448 0.4063316
## [442] 0.4064184 0.4065052 0.4065920 0.4066787 0.4067655 0.4068523 0.4069391
## [449] 0.4070258 0.4071126 0.4071994 0.4072862 0.4073730 0.4074597 0.4075465
## [456] 0.4076333 0.4077201 0.4078068 0.4078936 0.4079804 0.4080672 0.4081540
## [463] 0.4082407 0.4083275 0.4084143 0.4085011 0.4085878 0.4086746 0.4087614
## [470] 0.4088482 0.4089350 0.4090217 0.4091085 0.4091953 0.4092821 0.4093688
## [477] 0.4094556 0.4095424 0.4096292 0.4097160 0.4098027 0.4098895 0.4099763
## [484] 0.4100631 0.4101498 0.4102366 0.4103234 0.4104102 0.4104970 0.4105837
## [491] 0.4106705 0.4107573 0.4108441 0.4109308 0.4110176 0.4111044 0.4111912
## [498] 0.4112780 0.4113647 0.4114515 0.4115383 0.4116251 0.4117118 0.4117986
## [505] 0.4118854 0.4119722 0.4120590 0.4121457 0.4122325 0.4123193 0.4124061
## [512] 0.4124928 0.4125796 0.4126664 0.4127532 0.4128400 0.4129267 0.4130135
## [519] 0.4131003 0.4131871 0.4132738 0.4133606 0.4134474 0.4135342 0.4136210
## [526] 0.4137077 0.4137945 0.4138813 0.4139681 0.4140548 0.4141416 0.4142284
## [533] 0.4143152 0.4144020 0.4144887 0.4145755 0.4146623 0.4147491 0.4148358
## [540] 0.4149226 0.4150094 0.4150962 0.4151830 0.4152697 0.4153565 0.4154433
## [547] 0.4155301 0.4156168 0.4157036 0.4157904 0.4158772 0.4159640 0.4160507
## [554] 0.4161375 0.4162243 0.4163111 0.4163978 0.4164846 0.4165714 0.4166582
## [561] 0.4167450 0.4168317 0.4169185 0.4170053 0.4170921 0.4171788 0.4172656
## [568] 0.4173524 0.4174392 0.4175260 0.4176127 0.4176995 0.4177863 0.4178731
## [575] 0.4179598 0.4180466 0.4181334 0.4182202 0.4183070 0.4183937 0.4184805
## [582] 0.4185673 0.4186541 0.4187408 0.4188276 0.4189144 0.4190012 0.4190880
## [589] 0.4191747 0.4192615 0.4193483 0.4194351 0.4195218 0.4196086 0.4196954
## [596] 0.4197822 0.4198690 0.4199557 0.4200425 0.4201293 0.4202161 0.4203028
## [603] 0.4203896 0.4204764 0.4205632 0.4206500 0.4207367 0.4208235 0.4209103
## [610] 0.4209971 0.4210838 0.4211706 0.4212574 0.4213442 0.4214310 0.4215177
## [617] 0.4216045 0.4216913 0.4217781 0.4218648 0.4219516 0.4220384 0.4221252
## [624] 0.4222120 0.4222987 0.4223855 0.4224723 0.4225591 0.4226458 0.4227326
## [631] 0.4228194 0.4229062 0.4229930 0.4230797 0.4231665 0.4232533 0.4233401
## [638] 0.4234268 0.4235136 0.4236004 0.4236872 0.4237740 0.4238607 0.4239475
## [645] 0.4240343 0.4241211 0.4242078 0.4242946 0.4243814 0.4244682 0.4245550
## [652] 0.4246417 0.4247285 0.4248153 0.4249021 0.4249810 0.4250600 0.4251390
## [659] 0.4252179 0.4252969 0.4253759 0.4254548 0.4255338 0.4256128 0.4256917
## [666] 0.4257707 0.4258497 0.4259286 0.4260076 0.4260866 0.4261655 0.4262445
## [673] 0.4263235 0.4264024 0.4264814 0.4265604 0.4266393 0.4267183 0.4267973
## [680] 0.4268762 0.4269552 0.4270342 0.4271131 0.4271921 0.4272711 0.4273500
## [687] 0.4274290 0.4275080 0.4275869 0.4276659 0.4277449 0.4278238 0.4279028
## [694] 0.4279818 0.4280607 0.4281397 0.4282187 0.4282976 0.4283766 0.4284555
## [701] 0.4285345 0.4285939 0.4286534 0.4287128 0.4287722 0.4288316 0.4288911
## [708] 0.4289505 0.4290099 0.4290693 0.4291287 0.4291882 0.4292476 0.4293070
## [715] 0.4293664 0.4294259 0.4294853 0.4295447 0.4296041 0.4296635 0.4297230
## [722] 0.4297824 0.4298418 0.4299012 0.4299607 0.4300201 0.4300795 0.4301389
## [729] 0.4301984 0.4302578 0.4303172 0.4303766 0.4304360 0.4304955 0.4305549
## [736] 0.4306143 0.4306737 0.4307332 0.4307926 0.4308520 0.4309114 0.4309708
## [743] 0.4310303 0.4310897 0.4311491 0.4312085 0.4312680 0.4313274 0.4313868
## [750] 0.4314462 0.4315057 0.4315651 0.4316245 0.4316839 0.4317433 0.4318028
## [757] 0.4318622 0.4319216 0.4319810 0.4320405 0.4320999 0.4321593 0.4322187
## [764] 0.4322781 0.4323376 0.4323970 0.4324564 0.4325158 0.4325753 0.4326347
## [771] 0.4326941 0.4327535 0.4328130 0.4328724 0.4329318 0.4329912 0.4330506
## [778] 0.4331101 0.4331695 0.4332289 0.4332883 0.4333478 0.4334072 0.4334666
## [785] 0.4335260 0.4335855 0.4336449 0.4337043 0.4337637 0.4338231 0.4338826
## [792] 0.4339420 0.4340014 0.4340608 0.4341203 0.4341797 0.4342391 0.4342985
## [799] 0.4343579 0.4344174 0.4344768 0.4345362 0.4345956 0.4346551 0.4347145
## [806] 0.4347739 0.4348333 0.4348928 0.4349522 0.4350116 0.4350710 0.4351304
## [813] 0.4351899 0.4352493 0.4353087 0.4353681 0.4354276 0.4354870 0.4355464
## [820] 0.4356058 0.4356653 0.4357247 0.4357841 0.4358435 0.4359029 0.4359624
## [827] 0.4360218 0.4360812 0.4361406 0.4362001 0.4362595 0.4363189 0.4363783
## [834] 0.4364377 0.4364972 0.4365566 0.4366160 0.4366754 0.4367349 0.4367943
## [841] 0.4368537 0.4369184 0.4369831 0.4370478 0.4371125 0.4371772 0.4372419
## [848] 0.4373066 0.4373713 0.4374360 0.4375007 0.4375654 0.4376301 0.4376948
## [855] 0.4377595 0.4378242 0.4378888 0.4379535 0.4380182 0.4380829 0.4381476
## [862] 0.4382123 0.4382770 0.4383417 0.4384064 0.4384711 0.4385358 0.4386005
## [869] 0.4386652 0.4387299 0.4387946 0.4388593 0.4389240 0.4389887 0.4390534
## [876] 0.4391181 0.4391828 0.4392475 0.4393122 0.4393769 0.4394416 0.4395063
## [883] 0.4395709 0.4396356 0.4397003 0.4397650 0.4398297 0.4398944 0.4399615
## [890] 0.4400286 0.4400956 0.4401627 0.4402298 0.4402969 0.4403639 0.4404310
## [897] 0.4404981 0.4405652 0.4406322 0.4406993 0.4407664 0.4408335 0.4409005
## [904] 0.4409676 0.4410347 0.4411018 0.4411688 0.4412359 0.4413030 0.4413700
## [911] 0.4414371 0.4415042 0.4415713 0.4416383 0.4417054 0.4417725 0.4418396
## [918] 0.4419066 0.4419737 0.4420408 0.4421079 0.4421749 0.4422420 0.4423091
## [925] 0.4423761 0.4424432 0.4425103 0.4425774 0.4426444 0.4427115 0.4427786
## [932] 0.4428457 0.4429127 0.4429798 0.4430469 0.4431470 0.4432471 0.4433472
## [939] 0.4434473 0.4435474 0.4436476 0.4437477 0.4438478 0.4439479 0.4440480
## [946] 0.4441481 0.4442482 0.4443483 0.4444484 0.4445486 0.4446487 0.4447488
## [953] 0.4448489 0.4449490 0.4450491 0.4451492 0.4452493 0.4453494 0.4454496
## [960] 0.4455497 0.4456498 0.4457499 0.4458500 0.4459501 0.4460502 0.4461503
## [967] 0.4462504 0.4463505 0.4464507 0.4465508 0.4466509 0.4467510 0.4468511
## [974] 0.4469512 0.4470513 0.4471514 0.4472515 0.4473517 0.4474518 0.4475519
## [981] 0.4476520 0.4478047 0.4479574 0.4481101 0.4482628 0.4484155 0.4485682
## [988] 0.4487210 0.4488737 0.4490264 0.4491791 0.4493318 0.4494845 0.4496372
## [995] 0.4497899 0.4499426 0.4500953 0.4502480 0.4504008 0.4505535 0.4507062
## [1002] 0.4508589 0.4510116 0.4511643 0.4513170 0.4514697 0.4516224 0.4517751
## [1009] 0.4519278 0.4520806 0.4522333 0.4523860 0.4525387 0.4526914 0.4528441
## [1016] 0.4529968 0.4531495 0.4533022 0.4534549 0.4536076 0.4537604 0.4539131
## [1023] 0.4540658 0.4542185 0.4543712 0.4545239 0.4546766 0.4548293 0.4549993
## [1030] 0.4551693 0.4553393 0.4555093 0.4556793 0.4558492 0.4560192 0.4561892
## [1037] 0.4563592 0.4565292 0.4566992 0.4568692 0.4570391 0.4572091 0.4573791
## [1044] 0.4575491 0.4577191 0.4578891 0.4580591 0.4582291 0.4583990 0.4585690
## [1051] 0.4587390 0.4589090 0.4590790 0.4592490 0.4594190 0.4595889 0.4597589
## [1058] 0.4599289 0.4600989 0.4602689 0.4604389 0.4606089 0.4607789 0.4609488
## [1065] 0.4611188 0.4612888 0.4614588 0.4616288 0.4617988 0.4619688 0.4621387
## [1072] 0.4623087 0.4624787 0.4626487 0.4628187 0.4629887 0.4631587 0.4633287
## [1079] 0.4634986 0.4636686 0.4638386 0.4640086 0.4641786 0.4643486 0.4645186
## [1086] 0.4646885 0.4648585 0.4650285 0.4651985 0.4653685 0.4655385 0.4657085
## [1093] 0.4658785 0.4660484 0.4662184 0.4663884 0.4665584 0.4667284 0.4668984
## [1100] 0.4670684 0.4672383 0.4674083 0.4675783 0.4677483 0.4679183 0.4680883
## [1107] 0.4682583 0.4684283 0.4685982 0.4687682 0.4689382 0.4691082 0.4692782
## [1114] 0.4694482 0.4696182 0.4697881 0.4699581 0.4701281 0.4702981 0.4704681
## [1121] 0.4706381 0.4708081 0.4709781 0.4711480 0.4713180 0.4714880 0.4716580
## [1128] 0.4718280 0.4719980 0.4721680 0.4723379 0.4725079 0.4726779 0.4728479
## [1135] 0.4730179 0.4731879 0.4733579 0.4735279 0.4736978 0.4738678 0.4740378
## [1142] 0.4742078 0.4743778 0.4745478 0.4747178 0.4748877 0.4750577 0.4752277
## [1149] 0.4753977 0.4755677 0.4757377 0.4759077 0.4760777 0.4762476 0.4764176
## [1156] 0.4765876 0.4767576 0.4769276 0.4770976 0.4772676 0.4774375 0.4776075
## [1163] 0.4777775 0.4779475 0.4781175 0.4782875 0.4784575 0.4786275 0.4787530
## [1170] 0.4788785 0.4790041 0.4791296 0.4792551 0.4793807 0.4795062 0.4796317
## [1177] 0.4797573 0.4798828 0.4800084 0.4801339 0.4802594 0.4803850 0.4805105
## [1184] 0.4806360 0.4807616 0.4808871 0.4810126 0.4811382 0.4812637 0.4813892
## [1191] 0.4815148 0.4816403 0.4817659 0.4818914 0.4820169 0.4821425 0.4822680
## [1198] 0.4823935 0.4825191 0.4826446 0.4827701 0.4828957 0.4830212 0.4831468
## [1205] 0.4832723 0.4833978 0.4835234 0.4836489 0.4837744 0.4839000 0.4840255
## [1212] 0.4841510 0.4842766 0.4844021 0.4845277 0.4846532 0.4847787 0.4849043
## [1219] 0.4850298 0.4851553 0.4852809 0.4854064 0.4855319 0.4856575 0.4857830
## [1226] 0.4859086 0.4860341 0.4861596 0.4862852 0.4864107 0.4865362 0.4866618
## [1233] 0.4867873 0.4869128 0.4870384 0.4871639 0.4872894 0.4874150 0.4875405
## [1240] 0.4876661 0.4877916 0.4879171 0.4880427 0.4881682 0.4882937 0.4884193
## [1247] 0.4885448 0.4886703 0.4887959 0.4889214 0.4890470 0.4891725 0.4892980
## [1254] 0.4894236 0.4895491 0.4896746 0.4898002 0.4899257 0.4900512 0.4901768
## [1261] 0.4903023 0.4904279 0.4905534 0.4906789 0.4908045 0.4909300 0.4910555
## [1268] 0.4911811 0.4913066 0.4914321 0.4915577 0.4916832 0.4918088 0.4919343
## [1275] 0.4920598 0.4921854 0.4923109 0.4924364 0.4925620 0.4926875 0.4928130
## [1282] 0.4929386 0.4930641 0.4931896 0.4933152 0.4934407 0.4935663 0.4936918
## [1289] 0.4938173 0.4939429 0.4940684 0.4941939 0.4943195 0.4944450 0.4945705
## [1296] 0.4946961 0.4948216 0.4949472 0.4950727 0.4951982 0.4953238 0.4954493
## [1303] 0.4955748 0.4957004 0.4958259 0.4959514 0.4960770 0.4962025 0.4963281
## [1310] 0.4964536 0.4965791 0.4967047 0.4968302 0.4969557 0.4970813 0.4972068
## [1317] 0.4973323 0.4974579 0.4975834 0.4977090 0.4978345 0.4979600 0.4980856
## [1324] 0.4982111 0.4983366 0.4984622 0.4985877 0.4987132 0.4988388 0.4989643
## [1331] 0.4990898 0.4992154 0.4993409 0.4994665 0.4995920 0.4997175 0.4998431
## [1338] 0.4999686 0.5000941 0.5002197 0.5003452 0.5004707 0.5005963 0.5007218
## [1345] 0.5008474 0.5009729 0.5010984 0.5012240 0.5013495 0.5014750 0.5016006
## [1352] 0.5017261 0.5018516 0.5019772 0.5021027 0.5022283 0.5023538 0.5024793
## [1359] 0.5026049 0.5027304 0.5028559 0.5029815 0.5031070 0.5032325 0.5033581
## [1366] 0.5034836 0.5036092 0.5037347 0.5038602 0.5039858 0.5041113 0.5042368
## [1373] 0.5043624 0.5044879 0.5046134 0.5047390 0.5048645 0.5049900 0.5051156
## [1380] 0.5052411 0.5053667 0.5054922 0.5056177 0.5057433 0.5058688 0.5059943
## [1387] 0.5061199 0.5062454 0.5063709 0.5064965 0.5066220 0.5067476 0.5068731
## [1394] 0.5069986 0.5071242 0.5072497 0.5073752 0.5075008 0.5076263 0.5077518
## [1401] 0.5078774 0.5080029 0.5081285 0.5082540 0.5083795 0.5085051 0.5086306
## [1408] 0.5087561 0.5088817 0.5090072 0.5091327 0.5092583 0.5093838 0.5095094
## [1415] 0.5096349 0.5097604 0.5098860 0.5100115 0.5101370 0.5102626 0.5103881
## [1422] 0.5105136 0.5106392 0.5107647 0.5108902 0.5110158 0.5111413 0.5112669
## [1429] 0.5113924 0.5115179 0.5116435 0.5117690 0.5118945 0.5120201 0.5121456
## [1436] 0.5122711 0.5123967 0.5125222 0.5126478 0.5127733 0.5128988 0.5130244
## [1443] 0.5131499 0.5132754 0.5134010 0.5135265 0.5136520 0.5137776 0.5139031
## [1450] 0.5140287 0.5141542 0.5142797 0.5144053 0.5145308 0.5146563 0.5147819
## [1457] 0.5149074 0.5150329 0.5151585 0.5152840 0.5154095
##
##
## $history
## # A tibble: 1,461 x 5
## ds y floor t y_scaled
## <dttm> <dbl> <dbl> <dbl> <dbl>
## 1 2013-01-01 00:00:00 1588 0 0 0.317
## 2 2013-01-02 00:00:00 1538 0 0.000685 0.307
## 3 2013-01-03 00:00:00 1635 0 0.00137 0.327
## 4 2013-01-04 00:00:00 1741 0 0.00205 0.348
## 5 2013-01-05 00:00:00 1887 0 0.00274 0.377
## 6 2013-01-06 00:00:00 1956 0 0.00342 0.391
## 7 2013-01-07 00:00:00 1313 0 0.00411 0.262
## 8 2013-01-08 00:00:00 1538 0 0.00479 0.307
## 9 2013-01-09 00:00:00 1633 0 0.00548 0.326
## 10 2013-01-10 00:00:00 1677 0 0.00616 0.335
## # ... with 1,451 more rows
##
## $history.dates
## [1] "2013-01-01 GMT" "2013-01-02 GMT" "2013-01-03 GMT" "2013-01-04 GMT"
## [5] "2013-01-05 GMT" "2013-01-06 GMT" "2013-01-07 GMT" "2013-01-08 GMT"
## [9] "2013-01-09 GMT" "2013-01-10 GMT" "2013-01-11 GMT" "2013-01-12 GMT"
## [13] "2013-01-13 GMT" "2013-01-14 GMT" "2013-01-15 GMT" "2013-01-16 GMT"
## [17] "2013-01-17 GMT" "2013-01-18 GMT" "2013-01-19 GMT" "2013-01-20 GMT"
## [21] "2013-01-21 GMT" "2013-01-22 GMT" "2013-01-23 GMT" "2013-01-24 GMT"
## [25] "2013-01-25 GMT" "2013-01-26 GMT" "2013-01-27 GMT" "2013-01-28 GMT"
## [29] "2013-01-29 GMT" "2013-01-30 GMT" "2013-01-31 GMT" "2013-02-01 GMT"
## [33] "2013-02-02 GMT" "2013-02-03 GMT" "2013-02-04 GMT" "2013-02-05 GMT"
## [37] "2013-02-06 GMT" "2013-02-07 GMT" "2013-02-08 GMT" "2013-02-09 GMT"
## [41] "2013-02-10 GMT" "2013-02-11 GMT" "2013-02-12 GMT" "2013-02-13 GMT"
## [45] "2013-02-14 GMT" "2013-02-15 GMT" "2013-02-16 GMT" "2013-02-17 GMT"
## [49] "2013-02-18 GMT" "2013-02-19 GMT" "2013-02-20 GMT" "2013-02-21 GMT"
## [53] "2013-02-22 GMT" "2013-02-23 GMT" "2013-02-24 GMT" "2013-02-25 GMT"
## [57] "2013-02-26 GMT" "2013-02-27 GMT" "2013-02-28 GMT" "2013-03-01 GMT"
## [61] "2013-03-02 GMT" "2013-03-03 GMT" "2013-03-04 GMT" "2013-03-05 GMT"
## [65] "2013-03-06 GMT" "2013-03-07 GMT" "2013-03-08 GMT" "2013-03-09 GMT"
## [69] "2013-03-10 GMT" "2013-03-11 GMT" "2013-03-12 GMT" "2013-03-13 GMT"
## [73] "2013-03-14 GMT" "2013-03-15 GMT" "2013-03-16 GMT" "2013-03-17 GMT"
## [77] "2013-03-18 GMT" "2013-03-19 GMT" "2013-03-20 GMT" "2013-03-21 GMT"
## [81] "2013-03-22 GMT" "2013-03-23 GMT" "2013-03-24 GMT" "2013-03-25 GMT"
## [85] "2013-03-26 GMT" "2013-03-27 GMT" "2013-03-28 GMT" "2013-03-29 GMT"
## [89] "2013-03-30 GMT" "2013-03-31 GMT" "2013-04-01 GMT" "2013-04-02 GMT"
## [93] "2013-04-03 GMT" "2013-04-04 GMT" "2013-04-05 GMT" "2013-04-06 GMT"
## [97] "2013-04-07 GMT" "2013-04-08 GMT" "2013-04-09 GMT" "2013-04-10 GMT"
## [101] "2013-04-11 GMT" "2013-04-12 GMT" "2013-04-13 GMT" "2013-04-14 GMT"
## [105] "2013-04-15 GMT" "2013-04-16 GMT" "2013-04-17 GMT" "2013-04-18 GMT"
## [109] "2013-04-19 GMT" "2013-04-20 GMT" "2013-04-21 GMT" "2013-04-22 GMT"
## [113] "2013-04-23 GMT" "2013-04-24 GMT" "2013-04-25 GMT" "2013-04-26 GMT"
## [117] "2013-04-27 GMT" "2013-04-28 GMT" "2013-04-29 GMT" "2013-04-30 GMT"
## [121] "2013-05-01 GMT" "2013-05-02 GMT" "2013-05-03 GMT" "2013-05-04 GMT"
## [125] "2013-05-05 GMT" "2013-05-06 GMT" "2013-05-07 GMT" "2013-05-08 GMT"
## [129] "2013-05-09 GMT" "2013-05-10 GMT" "2013-05-11 GMT" "2013-05-12 GMT"
## [133] "2013-05-13 GMT" "2013-05-14 GMT" "2013-05-15 GMT" "2013-05-16 GMT"
## [137] "2013-05-17 GMT" "2013-05-18 GMT" "2013-05-19 GMT" "2013-05-20 GMT"
## [141] "2013-05-21 GMT" "2013-05-22 GMT" "2013-05-23 GMT" "2013-05-24 GMT"
## [145] "2013-05-25 GMT" "2013-05-26 GMT" "2013-05-27 GMT" "2013-05-28 GMT"
## [149] "2013-05-29 GMT" "2013-05-30 GMT" "2013-05-31 GMT" "2013-06-01 GMT"
## [153] "2013-06-02 GMT" "2013-06-03 GMT" "2013-06-04 GMT" "2013-06-05 GMT"
## [157] "2013-06-06 GMT" "2013-06-07 GMT" "2013-06-08 GMT" "2013-06-09 GMT"
## [161] "2013-06-10 GMT" "2013-06-11 GMT" "2013-06-12 GMT" "2013-06-13 GMT"
## [165] "2013-06-14 GMT" "2013-06-15 GMT" "2013-06-16 GMT" "2013-06-17 GMT"
## [169] "2013-06-18 GMT" "2013-06-19 GMT" "2013-06-20 GMT" "2013-06-21 GMT"
## [173] "2013-06-22 GMT" "2013-06-23 GMT" "2013-06-24 GMT" "2013-06-25 GMT"
## [177] "2013-06-26 GMT" "2013-06-27 GMT" "2013-06-28 GMT" "2013-06-29 GMT"
## [181] "2013-06-30 GMT" "2013-07-01 GMT" "2013-07-02 GMT" "2013-07-03 GMT"
## [185] "2013-07-04 GMT" "2013-07-05 GMT" "2013-07-06 GMT" "2013-07-07 GMT"
## [189] "2013-07-08 GMT" "2013-07-09 GMT" "2013-07-10 GMT" "2013-07-11 GMT"
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##
## $train.holiday.names
## NULL
##
## $train.component.cols
## additive_terms daily weekly yearly multiplicative_terms
## 1 1 0 0 1 0
## 2 1 0 0 1 0
## 3 1 0 0 1 0
## 4 1 0 0 1 0
## 5 1 0 0 1 0
## 6 1 0 0 1 0
## 7 1 0 0 1 0
## 8 1 0 0 1 0
## 9 1 0 0 1 0
## 10 1 0 0 1 0
## 11 1 0 0 1 0
## 12 1 0 0 1 0
## 13 1 0 0 1 0
## 14 1 0 0 1 0
## 15 1 0 0 1 0
## 16 1 0 0 1 0
## 17 1 0 0 1 0
## 18 1 0 0 1 0
## 19 1 0 0 1 0
## 20 1 0 0 1 0
## 21 1 0 1 0 0
## 22 1 0 1 0 0
## 23 1 0 1 0 0
## 24 1 0 1 0 0
## 25 1 0 1 0 0
## 26 1 0 1 0 0
## 27 1 1 0 0 0
## 28 1 1 0 0 0
## 29 1 1 0 0 0
## 30 1 1 0 0 0
## 31 1 1 0 0 0
## 32 1 1 0 0 0
## 33 1 1 0 0 0
## 34 1 1 0 0 0
##
## $component.modes
## $component.modes$additive
## [1] "yearly" "weekly"
## [3] "daily" "additive_terms"
## [5] "extra_regressors_additive" "holidays"
##
## $component.modes$multiplicative
## [1] "multiplicative_terms" "extra_regressors_multiplicative"
##
##
## $fit.kwargs
## list()
##
## attr(,"class")
## [1] "prophet" "list"
Berdasarkan hasil fitting model diatas bisa dijelaslkan bahwa
model_ts sekarang menyimpan informasi data permintaan
harian pada store 03. Sehingga kita bisa gunakan untuk mengekstrak
informasi deret waktu tersebut untuk melakukan perkiraan selama periode
waktu yang bisa ditentukan. Misalnya kita akan memperkiraan permintaan
penjualan untuk 1 tahun kedepan. Utuk melakukan ini kita harus
menyiapkan data frame yang terdiri dari rentang waktu/tanggal mendatang
yang akan diperkirakan. Untungnya dalam prophet() sudah
menyediakan sebuah fungsi make_future_dataframe()
memudahkan kita untuk menyiapkan data tersebut.
range(train_daily_3$ds)
## [1] "2013-01-01" "2016-12-31"
Bisa dilihat bahwa jangka waktu prediksi mulai dari 2013 s/d 2016
Periode prediksi adalah 1 tahun kedepan atau 365 hari
# menyiapkan tanggal utk prediksi
future_ts <- make_future_dataframe(model_ts, periods = 365, freq = "day")
glimpse(future_ts)
## Rows: 1,826
## Columns: 1
## $ ds <dttm> 2013-01-01, 2013-01-02, 2013-01-03, 2013-01-04, 2013-01-05, 2013-0~
# visualisasi hasil forecasting
forecast_ts <- predict(model_ts, future_ts)
plot(model_ts, forecast_ts)
Bisa dilihat bahwa, gambar pada grafik yang berwarna biru menunjukkan hasil forecast yang sudah dilakukan. Titik hitam menunjukkan data dari mulai 2013 sampai 2016. Waktu biru yang tidak ada titik adalah perkiraan permintaan untuk 2017
Dengan prophet dimungkinkan kita memvisulisasikan berdasarkan trend, weekly, dan yearly. Default: - daily: sampling hourly, dan frequency 24 - weekly: sampling daily, dan frequency 7 - yearly: sampling daily dan frequency 365
#visualiasi komponen model
prophet_plot_components(model_ts, forecast_ts)
Berdasarkan hasil visualisasi diatas bisa disimpulkan sebagai berikut:
# forecast berdasarkan seasionality month (bulan)
model_ts_monthly <- prophet(changepoint.prior.scale = 0.05,
yearly.seasonality = FALSE) %>%
add_seasonality(name = "monthly", period = 30.5, fourier.order = 3) %>%
fit.prophet(train_daily_3)
## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
future_ts_monthly <- make_future_dataframe(model_ts_monthly, periods = 365)
forecast_ts_monthly <- predict(model_ts_monthly, future_ts_monthly)
prophet_plot_components(model_ts_monthly, forecast_ts_monthly)
Dalam kasus ini kita akan memvisualisasi tren permintaan dari awal tahun 2017 sampai akhir 2017
#visualisasi dari tren awal 2017 sampai akhir 2017
plot(model_ts_monthly, forecast_ts_monthly)
Bisa dilihat bahwa terjadi nya trend peningkatan permintaan yang relatif tinggi dibandingkan tahun sebelumnya
# Menetapkan hari libur mulai dari tahun 2013 sampai 2016, misal libur di hari natal 25 desember atau tahun baru setiap tanggal 31 desember
holiday <-
data.frame(
holiday = "newyeareve",
ds = dmy(c("31-12-2013","31-12-2014", "31-12-2015", "31-12-2016", "31-12-2017")),
lower_window = -5,
upper_window = 0
)
holiday
# visualisasi hasil forecast dengan penambahan efek holiday
model_ts_holiday <- prophet(changepoint.prior.scale = 0.05,
holidays = holiday) %>%
add_seasonality(name = "monthly", period = 30.5, fourier.order = 5) %>%
fit.prophet(train_daily_3)
## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
future_ts_holiday <- make_future_dataframe(model_ts_holiday, periods = 365)
forecast_ts_holiday <- predict(model_ts_holiday, future_ts_holiday)
plot(model_ts_holiday, forecast_ts_holiday)
# melihat trend dan holiday effect dari perkiraan
prophet_plot_components(model_ts_holiday, forecast_ts_holiday)
Berdasarkan hasil visualisasi diatas bisa disimpulkan sebagai berikut:
forecast_ts %>%
select(ds, trend, weekly, yearly, yhat)
Ini digunakan untuk melihat trend perkiraan dengan bentuk lain yaitu dengan menambahkan changepoint
plot(model_ts, forecast_ts) +
add_changepoints_to_plot(model_ts, threshold = 0)
Garis merah putus-putus menunjukkan change point dari trend
before_2017 <- daily_demandstore03 %>%
mutate(
year = year(date)
) %>%
filter(year < 2017) %>%
rename(
ds = "date",
y = "demand"
)
after_2017 <- daily_demandstore03 %>%
mutate(
year = year(date)
) %>%
filter(year >= 2017) %>%
rename(
ds = "date",
y = "demand"
)
ggplot(before_2017, aes(x=ds, y=y)) +
geom_point() +
theme_minimal()
# Model sebelum 2017 dan visualisasinya
model_before_2017 <- prophet(yearly.seasonality = TRUE,
changepoint.prior.scale = 0.01) %>%
fit.prophet(before_2017)
## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
future_before_2017 <- make_future_dataframe(model_before_2017, periods = 365)
forecaset_before_2017 <- predict(model_before_2017, future_before_2017)
plot(model_before_2017, forecaset_before_2017) +
add_changepoints_to_plot(model_before_2017) +
geom_point(data = after_2017, aes(x = as.POSIXct(ds), y=y), color = "tomato3")
# Melihat transaksi paling banyak dalam satu minggu
forecast_ts %>%
mutate(
weekday = wday(ds, label = TRUE),
weekly = round(weekly, 5)
) %>%
filter(ds <= max(daily_demandstore03$date)) %>%
select(weekday, weekly) %>%
distinct() %>%
arrange(-weekly)
## Warning in base::check_tzones(e1, e2): 'tzone' attributes are inconsistent
# Visualisasi Model Sebelum Tahun 2017 berdasarkan hari dalam satu minggu
daily_demandstore03 %>%
mutate(
wday = wday(date, label = TRUE)
) %>%
ggplot(aes(x=date, y=demand)) +
geom_point(aes(color=wday))
Berdasarkan visualisasi diatas dapat disumpulan bahwa penjualan tertinggi pada tiap tahun ada pada hari Jumat, Sabtu dan Minggu
Untuk melakukan evaluasi dari model yang sudah disiapkan, maka kita bisa menguji model tersebut pada data testing.
# Menyiapkan data
test <- read.csv("data/test.csv")
glimpse(test)
## Rows: 182,500
## Columns: 4
## $ date <chr> "2017-01-01", "2017-01-02", "2017-01-03", "2017-01-04", "2017-01~
## $ store <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ item <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ sales <int> 19, 15, 10, 16, 14, 24, 14, 20, 18, 11, 14, 17, 7, 16, 29, 15, 1~
ada 182500 baris dan 4 kolom untuk data testing
# Merubah type data tanggal menjadi date
test %>%
mutate (date = as.Date(date)) %>%
group_by(date) %>%
summarise(
demand=sum(sales)
)
Bisa dilihat bahwa semua data testing ada pada tahun 2017.
Kita akan bandingkan data set Test dengan data set Training utk data sebelum tahun 2018, karena data train hanya sampai akhir 2016
cutoff <- dmy("01-01-2016")
train <- daily_demandstore03 %>%
filter(
date < cutoff
) %>%
rename(
"ds" = date,
"y" = demand
)
test <- daily_demandstore03 %>%
filter(
date >= cutoff
) %>%
rename(
"ds" = date,
"y" = demand
)
ggplot(daily_demandstore03, aes(x=date, y=demand)) +
geom_point(data = train, aes(x=ds, y=y)) +
geom_point(data = test, aes(x=ds, y=y), color="tomato3")
Warna hitam adalah data training dan warna merah adalah data testing
Model final digunakan untuk mempredisi data testing
# Menyiapkan model final
model_final <- prophet(changepoint.prior.scale = 0.05,
yearly.seasonality = TRUE,
holidays = holiday) %>%
add_seasonality(name = "monthly", period = 30.5, fourier.order = 5) %>%
fit.prophet(train)
## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.
future_final <- make_future_dataframe(model_final, periods = nrow(test) + 1)
forecast_final <- predict(model_final, future_final)
plot(model_final, forecast_final)
plot(model_final, forecast_final) +
geom_point(data = test %>%
mutate(ds = as.POSIXct(ds)), aes(x=ds, y=y), color="tomato3")
Bisa dilihat bahwa model dapat memprediksi data testing dan sama dengan trend yang sudah diperkirakan sebelumnya.
Untuk menentukan tingkat akurasi model, biasanya menghitung terlebih dulu nilai MAPE dari model. MAPE adalah Mean Absolute Persentase Error biasanya digunakan mengavaluasi model deret waktu.
eval <- test %>%
mutate(
ds = as.POSIXct(ds)
) %>%
left_join(forecast_final) %>%
select(ds, y, yhat, yhat_upper, yhat_lower)
## Joining, by = "ds"
eval
Untuk mendapatkan nilai mape kita harus mengurangi nilai sebenarnya
dengan nilai yang ada pada data testing (yhat) yang ada dalam data frame
forecast_final
mape <- function(y, yhat) {
return(mean(abs(y - yhat)/ y))
}
mape(eval$y, eval$yhat)
## [1] 0.04432686
Bisa dilihat bahwa nilai MAPE dari model adalah 0.04, sehingga akurasi dari model adalah 0,96 (96%). Jadi bisa disimpulkan bahwa model sangat akurat dalam melakukan prediksi.